a-young-woman-at-a-carnival-steps-up-to-the-high-striker-a-popular-test-of-strength-where-the-contes

Question

A young woman at a carnival steps up to the "high striker," a popular test of strength where the contestant hits one end of a lever with a mallet, propelling a small metal plug upward toward a bell. She gives the mallet a mighty swing and sends the plug to the top of the striker, where it rings the bell. FlGURE $2-42$ shows the corresponding position-versus-time plot for the plug. Using the information given in the plot, answer the following questions: (a) What is the average speed of the plug during its upward journey? (b) By how much does the speed of the plug decrease during its upward journey? (c) What is the initial speed of the plug? (Assume the plug is in free fall during its upward motion,
with no effects of air resistance or friction.)

Nathan Silvano · Accepted Answer

Okay, So in this problem, we have a figure. The represents movement of a glug in a high strike going fist on the graph. It&#x27;s something like this. He is your 0.6 in time and here, ISS for meters in the in the position position. Okay, so the first I think of the problem, we want to discover the average its speed off the plug. We know that average speed is defined as the difference in position, divided by the difference in time. So we just take the entire position off the block, the displacement just for divided by the difference in time. 0.6. So this is equal to six points, 67 meters per second. Second item of the problem. We need to discover how much the speed of the blood decrease during its motion of point. Okay, so we know that the difference in speed can be calculated. The difference and speech can be calculated. Us g times t. So the difference in speech it&#x27;s going to be 9.81 times 0.6. This is it close to difference in speed going to be five 0.885 point eight eight meters for a second. That&#x27;s the answer to the second I. Turn of the problem deterred itin of the problem. We need to calculate the initial velocity off the plug and to calculate initial velocity of the plug. Just needs to use def creation. The the that describes the position of the book as a function off time. Because any order equation we have one more quantity that we don&#x27;t know example. If we try to use VEHK, was the zero well us ut, we don&#x27;t have the final velocity, so the order to re creations are not going to solve this problem. That&#x27;s why we are using the position as a function of time. Okay, so let&#x27;s calculate this. The position is just four meters. Initial velocity we want to discover the time is 0.6. So here we have a negative gravity&#x27;s separation 9.81. Anyone divided by two times 0.6 square. So finally, the initial velocity off the plug is going to be 9.6 meters per second. That&#x27;s the final answer. Thanks for watching

Tomi Obadiya · Answer

Okay, um, this question married Bill Swing saw for Trump Peas towards Boban. Bobby&#x27;s 16 point run meat as we in the practical direction. It 16.0.2 meters away in the original direction. We&#x27;re waiting to catch Mary Bell on the first part of this question. Ax ask. So, so calculates the vera. Still projection for Mayor Bill I in the shell for the city on DDE. We called out the notes Onda. We know that vino has its Kong company entity a result for a ninja particle direction on for the resumes. So direction we not x is just gonna be court be nods coast firstly traded grace co sign because cause I know this gives off the artists into the uncle. I never cared for the larger sense to the judge since sido de, uh, Any shell velocity Veena? Why equals toe feed? Not saying 53 signed because sign always gives us the opposite. We&#x27;re looking for the Earl present company to impose its sight. I&#x27;m device cool company off the initial lost velocity. Um, we know something. We know this is a project emotion in two dimensions. Um, the time it takes for Mirabelle to get Bob covering six point moment as a device called this direction. It&#x27;s the same time it takes for Mayor Bell to get Bob coverage in point to meet us in the or result of direction. So the first thing we do is variety question of motion, and I&#x27;ll start with the X axis to simplify this question, I&#x27;m gonna make this my origin, so x not. And why not? It&#x27;s just gonna be serious. So, um, Kitty, Stan&#x27;s ex my excellent. By this time, our excellent is serious. So I&#x27;m just gonna You&#x27;re is thesis. Excellent. Since it&#x27;s here, I&#x27;m going to x equal to feel not ex. Thanks. Time toast restoration. Ex direction Square, Right? Right, too. Now we are ignoring areas the stars. So, um, it means the this project could not So the rate, the horizontal direction, so e x zero. So this myth are ex. The courts will be not ex Dempsey on a concert for time from this equation. So time is just gonna be called to X. Goodbye, like V, not ex on which is you&#x27;re simply x to buy and buy. Be not course 53 degrees. Um, same thing. Applies also to the logical direction we can use it. Questions of motion. Okay, Relating thesaurus trial with vertical direction with the any shelf understand of article direction time. See, at a situation in device onto the past Isolation. Itwas contraction. So why equal to V Not why? Times time across the acid very show. And you bicycle direction and square right by two times square. Delighted by to the insulation in the viatical direction is Josie acid refueling due to gravity and then acts downwards. But our projectiles going on port. So they go in opposite directions. So it means our assertion is gonna be the negative off station to to grab Sophie. Why, It&#x27;s just gonna be 1/4 Veena. Why? Times time my house off. She c squared. If our projectile was going was projected downward stead. That situation here, why would be poor Steve&#x27;s? But the Semites projected all ports, so I didn&#x27;t answer gates. Laceration due to grab this is could be a section describes is gonna take a negative value here. We already know the value of our time, which is thesis I can plug in time here, component this value here. So why equal to if he not. Why? Time stakes? You&#x27;re right about the notes. X my nose off G ex squid. Bye bye. We&#x27;re not X. It&#x27;s quick. Um, said define this for the we know. You mean why? To be vey not sign. Fair. Same 53 convenient exit V notes cost 53. So I&#x27;m just gonna put these values here. Vino act is gonna take v notes. Question to three on video wise. Gonna take feed, Not sang 53. So that makes why Dick or two. The knot signed three to survive, you know. Course three time stakes. My us G ex quit divided by two. So we&#x27;re not square Course squared. 33 Okay, so I&#x27;m vino. It&#x27;s sending America. It&#x27;s also indicate denominator here said, cancels out on bond the definition off. Kind of an angle. So Santa is just simply the sign of the group. Do any by the cost of the uncle. So this is just simply Stan 53 7 53 divided by courtside trail. Just turned 53. So simplifying this, but it&#x27;s just gonna be time. 53 times eggs minus key. X squared there by two. We&#x27;re not square cost squared 53. Um, please. I&#x27;m gonna box this equation here because we&#x27;re gonna end up using it. Indeed, for part of this question, the front part of this question. So right now we have this equation that actually relates the three components that we know Which the forts company that we don&#x27;t know. So we know the, um, vice school position. Enough. Bob is a result. Our position. We know the angle of projection, and this is a constant. It&#x27;s 9.8, but we don&#x27;t know Deanie Shell, huh? Projection speed. And that&#x27;s what we&#x27;re gonna look for. So I&#x27;m going. So for me, not square. And to do that, I&#x27;m gonna bring these over to the other side of the equation of the equations I&#x27;m gonna have. Why? Mayors X turn three equal minus G ex squid to be not square Course credit grain on. Then I&#x27;m gonna want to Black. True by fee, not square. What? Piper said that Venus quakes. I&#x27;m gonna be not squared record too. No quarter Didn&#x27;t square times since a long time for sex. So Venus quite terms. Why? My ex turn? You&#x27;re three equal to minus G X squared when What? I ve not squared. Thes cancers were hitting on me toes, so I have two course squared 53. Then I&#x27;m gonna divide both sides by this file use here. So that&#x27;s gonna make my V notes. Quit. He called to minus G ex Quigg divided by true course square 53 into Why minus takes ton 53 To eliminates this negative sign to make it look more pretty odd because sometimes negative science confused. So I&#x27;m just gonna most true by miners long minus one, which is just want right, some conserving this equation. So you have enough square You quote my analyst times minus his post Its where you have GX squared divided by so mine. Instance wise minus y minus times minus x Done Fixed stories plus eccentric details. I&#x27;m gonna have to course. Squid 43 and two Extent. 53. My ex wife. So what we do now? Just pluck the values that we have. So Venus Square just gonna be 9.8 times hit 0.2 square divided by to co sign square 53 into it&#x27;s going to turn three miners six point run andi units also balance out right because this is in meters per square seconds on you multiplied by meters. You have me to square. What square seconds? Um, it must by by meter square. You have meter, cube pass. Quit seconds, and then you divide by meters. So you eventually house eventually has me Tess Cube pass. Quit second. Divided by meters. That&#x27;s me too. Square per second squared, which is even for philosophy. Squared away eventually. Find squared. Meters square, US second square. You have meters per seconds. Violence is up. So now we really run a program values on finding squares. So, Vivien no, it is just gonna be squared off. 9.8 times 8.2 square. Too quiet by. Thanks. Two costs. Question three into 8.2. Turn three minus c explain one. Venus is gonna be 10 points. 79 You can ask for seconds. So now we figured out the four spot to question and second part, Um, ask so sue, uh, calculate the mount. Your diversity at this point here just before brought catches Mary Bell. So you&#x27;re looking for the magnitude drastic here, So this is gonna be the final resting. Why? Cos hi. It&#x27;s gonna be the final burst in the X Company. But we know Veena Savina is getting points 79 meters per second. Um, Vienna eggs, the initial versed in history, actually show state in 0.79 course three, and that&#x27;s equal to 8.2 8.38 point three images per sevens on the initial study. What&#x27;s good? Direction is just Clinton for seven line signed 53 and that&#x27;s just equal to you. Have one 0.13 me does my seconds. So, um, what are we doing here? Is right out of the equation of motion that relates our final verse city with its initial velocity acceleration on time. So we have finalised e equal to initial velocity. Close as serious. You&#x27;re gonna make this generic archery twosome right now, Lieutenant General, from closer consideration underst time. So what we need to do forces find time. And we know that time in court for eggs divided by Reno takes and that&#x27;s just equal to it. Going to divided by 20. I&#x27;m close to one. The 0.9 kids, it&#x27;s seconds seconds. Yeah, because this isn&#x27;t meters, that this is in meters per seconds, so meters, meters per seconds, just seconds. Meet this council&#x27;s metered Sandra Afford to buy. They bypassed sequence in just seconds. So this is gonna be second our time, which is time took Mirabelle to go order it, Bob to get a bulb at the same time for the results of the bicycle components. So speaking a question of motion into the quote confidence, you have to finalist in the rascal direction. Go to the initial first e viatical direction. Oh my g t on the final adversity. The Xterra actually, because too, do you Nischelle versed in the Ex Direction, Post gas station and the extraction we treat Seo because it&#x27;s not sedation. Endure isn&#x27;t the director, so it&#x27;s just define overstate the extraction. It&#x27;s just a quarterly in the shelf. Thirsty. The ex direction so And that&#x27;s equal to Hicks. 0.3 meters for samples. Well, for view I defined as a first name. Why direction is gonna be 1/4. Here&#x27;s ever kinds. You want tea for the initial versteeg Glascow direction minus 9.8 times their point time 88 Okay. WeII used minus nine point. Because the acceleration exacerbation dudes crafted by scoring against gravity so it has six negative sign in front of me on the time. It&#x27;s the time for the emotion which is the same for the flight, school and nose and conference. So get out. Finally arrested last connection to be one point today two 98 So they might need you. But the final that our city is just gonna be. Bye, Tyra Soemadi Con Company. So it&#x27;s good TV ex squid Because your wife&#x27;s quit, then find the square. That&#x27;s, um, that&#x27;s gonna be Equality Square pointy squared, coz 1.3 to 9, it&#x27;s quit and that should give us it Points four meters per seconds. So we have the the competence of the final verse it to B B Y on Vieques. Are we trying to find the direction now? Which is where the argo between this company between Wien X on the result we already know we can use the conduct of the angles Fada he called to your proceed off that angle, which is really why write complete piece freeway So v y divided by v x. So Thea sure. See quote Julie, our time off vey wise. Ah, one point three two 98 on Vieques thes um, a plane tree. Sophia is just gonna be 1/4 to are kind of that is, like 21 degrees. So it means this angle here, the angle between the ears, the result tons off district complaints on the or his own. Tough is not one thief face grain of our To the thought question, We actually calculates the distance time graph for the two directions. The glass clatters air two directors and also the realistic time graph from two directions Arizona kind of logical directions. Somebody descends Time ground for the our results of direction So extreme. Andi, this is the time is the time at which Mary Bell gets about 0.98 seconds, which is close to one one seconds. Understand qualities a second. So the first me after the skies the question that governments emotion, injuries or two direction We know that text 1/4 V knots. Thanks. This time on, if you compare this with without a question of relying so why get called to mix Percy? Where? Why he is ex for us here on XY Ace. Time for us. Here we see that intercept which you see is just zero. It has to go to the origin. I will see that the slope which is came is venal X and the cost of I. Because Vienna exit procedure while I was just eight point treatment, ask for seconds. So it means it has to slope upwards. So we have a strict lie graph that slopes orc words. Similarly, the spaceman, But the distance time, Graham, you think that&#x27;s time graph for, um divide school more shine. We have to also look at the equation of motion that governs it. And that&#x27;s why I called to three knots. Quiet. Next time GT squared. So which is there? Uh, which is a parable of on my time when time he calls you po zero in here you get your white to Brazil, so it means it Asako truly origin on at small times the Lena part of time which is t is gonna be more dominant. Stand square, father. Right, because zero point five is greater than 0.5 square but us as time begins to elapse on time begins to get heart bigger, bigger than it is become small door minutes so that small sometimes you expected strip line. And then as time gets larger, you expect me to call. She&#x27;s quick This way. She&#x27;s It&#x27;s a parable. Um, for the first city time graph yours into direction. Sophie X. I&#x27;m see way Look at the equation. Emotion go once this motion on dust fee. Thanks. It&#x27;s just a court Trevino x So there&#x27;s no time comfort. So it means this motion doesn&#x27;t depend on time. So what would expect is a streetlight pilo to time axis because doesn&#x27;t get paid on time on this while you hear just re not ex, Okay? And then for the footman, we have the same thing that&#x27;s gonna go on cycle here. One sec, one here. It&#x27;s gonna be my time. It&#x27;s gonna be my view like so were Isaac. Question of motion. That&#x27;s V Why court Agreed not. Why? My nose key. So if we compare these without a question of your line, why he called to see Because that makes Yeah, I changed it because Xia corresponds so at a time. And this good Andrea White Christ superstar. Why, Despite Sophie notice Just feeling why shows the intercepts so somewhere here? Yeah, I&#x27;ve seen a glass, but then you see that slope? Is it negative slope because of this negative? Finally, here, minus tree. So that sloped downwards. So you&#x27;re expected. Straight line? The shows don&#x27;t know. It&#x27;s just like that, um, moving forward to the fourth part of this question. It say&#x27;s that Mary Bell onboard with practise in the night before and then Bob Field Suk archer. So maybe Bill has a projection. Same angle to treat the grace and would assume that she&#x27;s also moving with the initial speed. That recording fest. But in our state in part I said good night notice for seconds. She guys project that. Then Bob&#x27;s Soma here feels catcher A dent. She goes into a safety net. That is funny. Height. Is that a high 68.6 meters beetle? So somewhere here 0.6 meters. Andi, remember, this is our origin. Right? So on device collapses. All hides approve. Piece projection Plane is greater. General heights below Dese heights around this region are negative because yep, below zero Similarly lens in your isn&#x27;t the directions to the right. A post. He watched the left. I&#x27;m negative. So, um, become about two. The question we found area, which is why he called X con 53 minus G ex. Quit over. Ooh, two v not scram. Course quick theater v Not cost there. I just feed not ex Arizona component of peanuts. So we not squared, cause Quite fair. I just feel so exquisite. So why equal? Thanks. Huh? 53 mass g. Ex quick to be not Thanks. Script. The reason why we&#x27;re using these equations Because we No, the height of deception It&#x27;s it&#x27;s miners. It consists miners, because it&#x27;s below Merry bells projection. Clean on. Um um really, really looking for ex we nog. Now we know vinos X, you know, except Jersey resent our complaint or peace me Show projection. Speak. So, uh, what we do is we put enough values of minus 8.6. Don&#x27;t forget, it&#x27;s minus because it&#x27;s below. Maybe it was projection between minus 8.6 equal eggs the dungeon off 53. He&#x27;s ah, one point 327 My nose. 9.8. Ex squid derided by two times 8.3 squared. Who&#x27;s this? And that&#x27;s just simply huh. 32 seven eggs minus, um 9.82 right. By two times at 20.3 squared equal 0.7 long one ex quit so I can made this equation pretty. Um, um I&#x27;m just gonna fall right here so we don&#x27;t get confused to seven eggs, lands your crimes, Theo, several on. I&#x27;m gonna write this equation to make it look familiar. It&#x27;s a quadratic equation, and it might not be really obvious right now, but you might bring this value over here and bring this value away, and you could be equated to zero. Then we get to see, see more clearly. So this is gonna be 0.7 long, long ex squid bringing this guy over here minus 1.3 27 Thanks, Miners. 0.6 reporters here. Then I can divide true by 0.711 to make the coefficient off X square one just to simplify the question for So this is gonna be X squared minus 1.3 to 7 to eight by 0.7 More wrong. It&#x27;s just simply 18.66 18 0.66 Thanks minors. So 8.6. Divided by 0.71 He&#x27;s just one trying try me. 0.96 that call Syria. So this is a quadratic equation. It&#x27;s you recall, equip radically questions from a X squared minus B X Across sea you quarter they&#x27;re on the way we solve it is just using the quadratic from lower, which is this is both, Sir X A quote remind us Be person Miners squared, Be square minus for ABC. We&#x27;re about to a So that&#x27;s not a question. Here again, we have Thanks. Quick. Come, miners. 18 kind 666 My nose want training from 96 because they&#x27;re so this is gonna make our a culture one, which is questions off Eggs square on the question of exit B to be coach of minors 18.66 and see in court to minors 1 20 0.96 So solving this equation X is gonna be 1/4 to my the negative. Miners be just minus stamps. Miners 18.66 and US 18.6 is raising 0.66 close of miles squared off minus 18.60. Square 66 square is just 18.6 x squared because mine are squares. Boss Steve, So this is gonna be Hey, Chin front 66 Squared my hands. Full days long sees miners want training 196 divided by 282 times. One, which is just too so eggs Week or two. It&#x27;s in 0.66 person liners. Square ago by 66 Square is three for it clients. 20 crows, My nose times minus a sports saved us. Withers. Why we are responsive. A up four times one. Training for nice sixes for its 312 483 12 Do right by two. So that makes our eggs. Quote. Didn&#x27;t current 66 costs and Niners squared off the some of this value? 348.204483 point. Want to recall two. It&#x27;s 32.12 to run it by two. So thanks and culture. 18 0.66 Go serve Minors Squaring off his father here. He&#x27;s trying to 0.25 training training 0.8598 But Nate&#x27;s fine to my right. Soon. This means that you are thanks could be either 18 0.66 Mine. US. Training 0.85 Divided by 20 it seemed crane 66 plots trying it Plan? It&#x27;s five because I write too. So X a quote Negative. 5.0 95 meters. Oh, 23 for in 76 means is if you if you recall, um, this is this is our origin. Yeah. So do you. Negative values our values to the left on positive vibes. Injuries in two directions are advised to the right. So we just re God mine yours. Five points, you 95 Because that&#x27;s saying that maybe it was projected to the live, but we know she was projected to the right. So we expect the landing the safety net to be so ready. Not to the right, Celeste. 23 point several, six meters. Thank you.

Mihajlo Grcic · Answer

So in this problem we have a circus and Mary Bell performing a new circus act where she had have to project herself. Anthony had given angle and be called by. She&#x27;s expected to be caught by her partner, Bob. Now promotion can be model does project emotion. Therefore, her trajectory will be a problem. Now her project, The trajectory must intersect with a specific point. This base And this is the point where Bob stands. This point is given in the problem by these coordinates. And when 2 m x 6.1 m. Why? And this problem has four parts now for the party we need to solve for the initial velocity that she must have in order to reach Bob and time teeth time that it takes her to reach Bob. First, we need to derive the equation for the time since we have 21 knowns, we need two equations, and these equations can be derived from the vertical result in this place with promises. Now we could start from the vertical special function, which is why I&#x27;m here equals y zero. Plus we zero Why t minus g d squared over to. Since Mary is at the beginning of the coordinate system. Why zero will be equal to zero. And we&#x27;re only left with her vertical. I lost it there, but we really transformed this into a different form. We will respond is to re zero times Sinus state the scenes her. This is just the component off her initial vertical Austin. This is her initial Austin Times Sinus detail times here minus G d squared over health. Now the second equation is going to be from the horizontal displacement, so accept e equals zero x times a day, which can be expanded into zero. Co sign Tito Times D From here, you can see that the term with zero times T is equal to X alert. Co sign Tita and both X and call sent Ethan are known values. So this is useful, since we can direct subsidies substitute this into the vertical spaceman function. So in that case, why will be equal to now? Why zero? We are going to be X over. All sign the times scientific minus G d squared over do. And for these parts no, we can make a better hormone. X is going to be x times 10 Geant. Dave, this is signed over. Closest engine minus G D squared over two. We know why we know X. We know every terminus equation except for the C squared. And we will sold for titties. Quite so we will simply perform a series of alleged break transformations G The squared over two would be equal to eggs engine dita minus why and further we can say that d equals eggs 10 jin t the minus y times still over g and square of that. So let&#x27;s substitute the known values here we have for for the X while you will use simply 8.2 m tangent or 53 degrees minus 6.1 Peter&#x27;s times do over 9.81 m per second squared. This is this whole equation will going to seconds dimension. So this will be time. And when we put this Wallace into a calculator, we finally obtained that the equals 0.988 seconds. This is very important. We will use these time interval to plot the graphs or to sketch the graphs later. Now we console for free zero, you know, very straightforward manner since re zero times sting equals X over Go Saint Yves Moving tea together size Since we know they re zero will be equal to eggs. Over course I&#x27;m deep time steel which is equal do eight going to meters over Go sign 53 degrees times 0.98 they meters per second And finally we obtained that re zero equals 13 0.8 meters per second And now we have solved for the first part of the problem. Now for the part to be you&#x27;re asked for the final velocity. This is the velocity that Mary will have when she reaches Bob And for angle beat the prime That is the angle off the finally lost at which angle she will approach her partner Bob First people saw for components over the final we lost so component vertical Why? Where the Clipper bonus will be equal to initial particular Osti but white component with minus g d. Now the sti is the time we already evaluated in the apartheid with the problem simply substituting the known volumes. We see that this is equal to 13.8 times Sinus. You have to create degrees minus 989 The one thanks 0.988 dimensions off each term are going to be meeting second, and this is equal to 1.34 m per second. This is for the vertical component offered scores. Auto component. The final X is going to equal we zero acts, which is equal to 30 Go sign, Peter. And since we know we zero and go sign of Peter, we can simply substitute. This is 13 point. They go same or 53 degrees. And when we evaluate this calculator, we obtained the volley off 8.3 m per second. Now a final is going to be school. This is a picture Korean territory. Um and I will sketch later Why? We used exactly this for you&#x27;re going to use we final. Why squared? Pull us we final X squared. Why? Because if we look at the components of the final Willows Director, for example, like this, this is we final. This is going to be the vertical component. And this is going to be, for example, component. So really so. And also the angle here is Steve the prime now the from particular interior, um which we see obviously, why this is the proper formula and we can further evaluated us. Rieff equals substituted known bodies. This is going to be one 0.34. Maybe there&#x27;s a second squid Plus we&#x27;re integrating in America. So 8.3 squared meters per second and we obtained that the value is ah, final velocity we have is equal to eight 0.40 1 m Very second. This is of course, after after we put it put this into a calculator and for the angle. Well, obviously, if we divide, we have white over re FX. We can see this is excellent. Here we can see that this is going to be the tangent of the Tita Prime. And did the prime will be arc tinge off the If Really, why? Over were acts so we can to find that tangent. The prime is able to we Why over we, uh, eggs And therefore the supplies that the prime is are contingent off we Why? Over we x which equals, huh? Sandra Now we can substitute unknown values 1.4 over 8.3 and putting this into a calculator, we obtained that the angle off approach is going to be It&#x27;s expected to be 9.70 degrees. And here we have sold the part B. Now, for the part C on this problem, we need to sketch the graphs. So we&#x27;re not plotting the grafts. We&#x27;re just catching the graphs that the graph so horizontal and vertical displacements and velocity versus time. This is basically so why were sketching grass were sketching them to express some attributes of the functions. This is the difference between sketch a graph and actually plotting a graph. Now, this is going to be my tea and X. And if the point of time that we have found this here, this is 0.988 and the horizontal position is here says 8.2 m. This is their common point on the on the plane. The the horizontal displacement will just increase with time, but it will increase in a linear fashion. This will be just a straight line from here to this point, a straight line said, This is a linear function and this is what we&#x27;re trying to express with this graph. Now, for the second graph here, we&#x27;ll we&#x27;ll have why displacement on here? We will have time t also will plug the same point in time and here you well have a 0.6 point 1 m. Now, in this case, the function is not linear because the function why off the depends on the d squared. It has both t and t square terms. This is a polynomial and the graph of polynomial looks something like this. It is a non linear function. It has this Salo direction change and increase with Department of Teeth. And now for the other parts with the rest to graphs. We have the graph off horizontal the lost in component over time burst. This time let&#x27;s say here is time point And here is the ain&#x27;t 0.3 m per second. This is the horizontal velocity component. As we know there is no air resistance, so this component would not change in time. There is no account reiteration to decrease this velocity so this velocity will stay constant and on the graph, this is just a simple straight line like this under no inclination, Simplest, pro, too de flying and final sketch we need is this sketch off vertical the lost two component and I&#x27;m versus time. So if the time point is here. First, we need to know that we have a starting vertical Austin. This is going to be 11 102 meters per second and we have the final velocity. The final component found a vertical Austin component which is here, and we already evaluated. It does 1.34 m. Second, who were the vertical lost? It will drop down in a linear fashion because gravity is pulling married down and is decreasing her initial velocity. Her vertical component of the lost is going to be decreased because gravity is also in the acting in the vertical direction. So however lost, we can say that it will lean nearly, fall down, eat legged. It&#x27;s so from here to this point right here, this is This is a straight line. This is supposed to be a straight line of the graph, and this is to express that vertical velocity is decreasing in a linear fashion. It&#x27;s only depending on the tee. It is not depending on the square or any other more complicated functional for the Parliament 30 just on the and we have sketched every every drug that we need. So the part C or this problem is already so. And for the party now part of the when when the circus act is being actually performed, Mary is not that she doesn&#x27;t get called by Bob. Bob misses her and she falls to the safety nets. We know that the hate between her starting position and the safety nets, this is why to is going to be eight 0.6 m now since she&#x27;s falling down so below zero, she&#x27;s on zero vertical position and now she&#x27;s falling down from But that vertical position This is going to be a negative value, But so when we use this value in the equation or in the function, this is goingto have negative sign like in part A. We need soul for the time T. But in this case, we really don&#x27;t really need to two equations when only one equation and we will derive this equation from the second vertical this basement function. So why Off T, which is going to be equals minus y two will be equal to we zero t one. This is a different time, so because this is a different kind of motion, she missed Bob and this this time t one is the time it takes for her to reach the safety nets from her starting position. Off course, minus one half G D one square. Uh, here, this is Ah, of course. The initial vertical component off we lost. So we can simply substitute the Somalia&#x27;s. We have minus 8.6 here, and this is going to be equal to 13.8 times Sinus or 50 tree degrees, minus nine point 81/2. He&#x27;s one squared and also t one here. As you notice, this is a quadratic equation. So to put it in a proper form, a better form. In this case, we can say that nine 0.81 over to D one squared. This is a plus since we moved on the left hand side. Then we have a minus off 13.8 times Sinus, 53 degrees. The one and also minus 8.6 equals zero. This is going to be a this is going to be be. And this is going to be C. And this can be sold in two ways. You can either use a computer sulphur on simply, could A, B and C directly and he will give you toe solutions 41. Or you can use the quadratic formula with that is the one that could have two solutions. So this is one to the two solutions for the one did Toby minus B plus minus square root B squared, minus for a C over two A. And this is going to be really messy. Now, since we&#x27;re here this 13 times eight Sinus, 53 plus minus where the big square root 13 times eight Sinus, 53 degrees squared minus four times 9.81 or two over to and those who this is going to be a plus. I actually, because we can We&#x27;re multiplying it with a negative c. So this is a 16 here. All of this goes over 9.89. Since we&#x27;re just multiplying, it would do putting all this Wallace in a calculator and the value thing with plus and minus uses two solutions one positive and one negative solution. Off course time is always positive. So we take the positive solution and the positive solution will be that t one equals two point 86 seconds. Very important part of this problem. No horizontal displacement will be evaluated from the horizontal displacement function, which goes as, and this is also the maximal Caries. Until this basement as well. So say Max equals two, the horizontal velocity component times do you want and the Sequels to we already cock it. The presentable lost the component, so it is going to be 8.3 times two point 86 This is going to be in meters, and finally, maximal displacement is horizontally 20 tree 0.7 m. This is her displacement on the horizontal axis because she&#x27;s simultaneously moving vertical and horizontal. So first we evaluated for the time off the vertical displacement and then use the same exact exact time to evaluate for the horizontal displacement, using the known horizontal component off horizontal motion. Now the whole problem is sold. I hope that this was helpful and I expect to see you in the next video lesson by

Mayukh Banik · Answer

For this part, we have to balance the final kinetic energy half MV Square equal the initial potential energy MGH So we have V equals square root off G H. It was two times 9.8 meters for a second square times. The Heidi&#x27;s 14 meter swirled of that comes out to the 16.6 major for a second.

Averell Hause · Answer

Let&#x27;s first applied the conservation of energy in order to find the speed at the bottom of the pendulum or the bottom of the ride after it. Excuse me. After the ride is suspended motionless at the top of its park, we have potential energy and then at the bottom of the pendulum after the ride has been influenced by gravity At the bottom is all kinetic energy. And so we can then say that MGH is equaling 1/2 m V squared. Of course, masses cancel out and we have that the final velocity is equaling the square root of to G. H. We know that h in this case of simply gonna be the radius of the ride itself. So we consider the velocity would be equal in the square root of two times 9.8 meters per second squared multiplied by 14 meters, and this is giving us 16.6 meters per second. So that would be the linear speed, rather linear velocity at a point on the tip of the end of the 14 meter ride and radius and then for part A. If you want to find the central public celebration, this would be equal. The linear velocity squared, divided by the radius. So this would be 16 0.6 meters per second quantity squared, divided by 14 meters. And this is equaling 19.6 meters per second squared. So this would be the centripetal acceleration for party now for part B. Ah, they simply want us to draw uh, foot. Rather. My apologies. This would be for part B. This would be for part a and then for part c, they want us to simply draw free body diagram. So really, it&#x27;s only gonna be going up the force normal. Or you can say this capital end and then going down the weight or the force due to gravity. So we can say that then the net force is gonna be equal in the mass times the centripetal acceleration and then this is going to be equal to the normal force, minus the weight and so we can solve for the normal force. This would be equaling the mass times, the accelerant, the central acceleration, plus mg, and so we can solve the normal force would then be equaling the mass which we know to be 60 kilograms. This is before an average person at one times 19.6 plus 9.8 meters per second squared. And this is equaling 1.76 times 10 to the third Newton&#x27;s. This would be our answer for the normal force now continuing on for part C. We can have the normal force divided by the weight, which would give us the normal force in terms of, um, the weight felt due to gravity. So 1.76 times 10 to the third Newtons, divided by 60 kilograms, multiplied by 9.8 meters per second squared. And this is giving us 3.0 So essentially the normal force for the writer is three times the weight of gravity. So So when you&#x27;re on the ride, you actually feel like you&#x27;re under three times your own weight. Uh, when you are at the bottom of the right. So when you&#x27;re at the bottom of the soap of the essentially the pendulum Ah, you feel like you&#x27;re three times three times greater than your own rate than your own. Wait, wait. And then for part deed. Is this reasonable? Um, yeah. Um, it&#x27;s it&#x27;s reasonable in the fact that it&#x27;s on Lee three times. But, um, usually, but some of these rides don&#x27;t always. If you have the pendulum here and let&#x27;s just say this is the ship, they usually go up to a certain point. So let&#x27;s to say here or even here, they never really go in a full circle. They never really go in a four full circle. So this means that this centripetal acceleration might be a little bit less. But we can say for the sake of this question, yes. Uh, this seems reasonable, um, as the force felt. But the writer is not too great. Where we can say is three times the force of gravity. Now, anything more than this would be a bit dangerous in the sense that one might pass out on this ride. Because if you&#x27;re under extreme, um, pressures, you&#x27;re gonna, um you&#x27;re gonna blackout, and blood might rush to other parts of your body besides your brain, Um, and most rides, I would say, are a little bit less than 3.0, 3.0 But again, this is this seems reasonable for this type of ride. That is the end of the solution. Thank you for watching

Sheh Lit Chang · Answer

this question is about finding the speed off the projectile before the collision. So parts a, uh, the suspect that is using their ballistic pendulum set up so, uh, so realistic. Pendulum set up. Hey, this is in example, 9.6 in the textbook and the formula to calculate We want a is given s, um, and one plus and two You are by m one times square it to GH. Okay. Using the numbers given to us in one in 68.8 grams onto is 263 grams and then this thing is your body. You end up talking about 68.8 and then multiply by two GH square roots and then the each is given to be 8.68 c m. Okay, so when you calculate this, you get 6.29 meters per second. So this is the answer for parts A parts be used Another method to determine you want a which is so having a fortune some distance through a projectile motion. So we want a and then, uh, you so true projectile motion force your height, why and then go through some distance. X horizontal distance X think so we&#x27;ll be using, uh, yeah, Why equals two Ah, half G. Pataki Square. Okay, so don t I would just be, too. Why do? Bye bye tree. Okay. And then to calculate, we want a it&#x27;s just x divided by down 30. So this is just X, uh, the right by, uh, to why my buggy? And then this is the expression. Have you asked to appear? Yeah. Then, uh, given that So this is how we obtain this expression. Okay, then, given that X equals 257 cm, why is 85.3 cm? I came to find you on a This gives us converting them into s I units. Okay, they get 6.16 meters for a second. Okay, this is the answer for parts P. So we see that there is a difference between the two numbers that were calculated, Process A and B. So two accounts for the difference. So the additions are between, uh, answers in parts A and B que is around 2%. Okay, So most of the difference, uh, can be accounted for by the uncertainty off the data. OK, so the uncertainty of the data. Uh, so some things like that have you will be a sequel to, uh, 0.0 wine times. I do about 8.68 This is answering the the height regimen in part a. And then that&#x27;s also that&#x27;s in the measurement in the rest, for both objects. Okay. And then similarly, in part speed, this is the uncertainty in the ex measurement. And then this is the uncertainty in the wind measurement. When you calculate this, this is 1.1%. Okay, so that&#x27;s how we account for the difference in the two calculations.

Problem

While sitting on a tree branch 10.0 m above the g…

Problem 87 Hard Difficulty

Answer

a) 6.67 $\mathrm{m} / \mathrm{s}$
b) 5.88 $\mathrm{m} / \mathrm{s}$
c) 9.60 $\mathrm{m} / \mathrm{s}$

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Math Review - Intro

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a) 6.67 $\mathrm{m} / \mathrm{s}$b) 5.88 $\mathrm{m} / \mathrm{s}$c) 9.60 $\mathrm{m} / \mathrm{s}$

Physics

Zachary M.

Aspen F.

Jared E.

Meghan M.

Math Review - Intro

Algebra - Example 1

James S. WalkerPhysics

Zachary M.

Aspen F.

Jared E.

Meghan M.

a) 6.67 $\mathrm{m} / \mathrm{s}$
b) 5.88 $\mathrm{m} / \mathrm{s}$
c) 9.60 $\mathrm{m} / \mathrm{s}$

James S. Walker

Physics