a-0145-kg-baseball-is-travelling-at-40-mathrmm-mathrms-horizontally-when-it-is-struck-by-a-baseball-

Question

A 0.145 kg baseball is travelling at 40 $\mathrm{m} / \mathrm{s}$ horizontally when it is struck by a baseball bat. The baseball leaves the bat at 50 $\mathrm{m} / \mathrm{s}$ back in the direction it came from, but at an angle of $40^{\circ}$ above the horizontal. What is the magnitude of the impulse imparted to the baseball?
(A) 1.45 $\mathrm{N} \cdot \mathrm{s}$
(B) 4.66 $\mathrm{N} \cdot \mathrm{s}$
(C) 12.3 $\mathrm{N} \cdot \mathrm{S}$
(D) 13.1 $\mathrm{N} \cdot \mathrm{s}$

Vishal Gupta · Accepted Answer

Hi in the given problem mask off the baseball. It&#x27;s given S. M. is equal to 0.14 five kg. The speed with which it hits the bat moving horizontally here this is the direction of motion of this baseball And it is moving with the speed we I and its magnitude is given us 40 meter per second, after which it is reflected back with the speed we have having a magnitude of 50 meter per second, Making an angle of 40° with the horizontal. So it will be having two components one horizontal. Which will be given as we have because 40 degree and you do the opposite direction. It will be taken as negative and another component, vertical component means the component along this bat and that will be we have sign 40 degree. So the initial linear momentum of the baseball will be only along X. Axis means, or we can say along horizontal, but finally linear momentum will be along both directions. X. Axis and Y axis means along horizontal and vertical. Both so we have to find here the impulse imparted by the bed to the ball. So that impulse is actually the change in linear momentum. So to find time pulse magnitude of impulse, we have to find the change in living your momentum means it should be the final linear momentum. B two minus initial linear momentum. Even so, first of all we find the magnitude of changing linear momentum along X axis, then along Y axis. So first of all, delta P. X. Will be given us B. X. F means linear momentum. Final linear momentum along X axis minus initial linear momentum along X axis. So that is given as for final linear momentum, mass of the baseball will be multiplied with this component of velocity along X axis. So it comes out to be minus M. Into we F. Because 40 degrees. And for p excite this is mass of the baseball. But with we I It will be multiplied by the eye. Taking this mask as a comin out along with the negative sign here, this is minus M. We have cost 40 degree minus V. I. So finally plugging in all known values form us. This is 0.145 kilogram for VF. This is 50 in 2000 and 40 degree minus 40 m per second. So finally it comes out to be 0.246 Newton in two seconds. Now, for the change in leader momentum along y axis, it will be final linear momentum along Y axis means P Y F minus initial linear momentum along by excess PV II, which was zero. So for P Y F. It will be given as the product of mass with The vertical component of final velocity means this is we have signed 40°.. So, plugging in unknown values again, this is 0.145 kg for the mask for velocity this is 50 sign 40°.. Need a per second. And finally it comes out to be 4.66 New turn into second. So finally the magnitude of changing linear momentum. Or we can say the impulse that will be given us the square root of Squirtle, B X. Delta P X plus the square of delta P Y. So plugging in The found out values here for Delta P. Ecstasies zero point 246 to the whole square. And for Delta P by this is 4.66 to the whole square. So here it comes out to be 0.06 05 Plus 21.72 Newton in two seconds. Or we can say this is the square root of 21.78 new, turning to second. Or finally this is 4.66 Newton in two seconds. So we can see here our option B is correct. Thank you.

Kristela Garcia · Answer

and this problem. We have a baseball traveling horizontally at 40 meters per second, and it struck by that and the baseball leaves about in the same direction, but an angle of 40 degrees above the horizontal. So it goes back at 50 and it&#x27;s going to have an ankle above the horizontal of 40 degrees. So that means it&#x27;s going to have a velocity of the ex direction and a velocity in the wind direction. Now, if we look at our impulse, we&#x27;re going to have an impulse in both E X and the wind direction. So this is our mass times Change in velocity in the extraction and our mass times change in velocity in the wind direction. So in the ex direction we have 0.145 Our final velocity is 50 co sign of 40 so negative 50 co sign of 40 minus 40 gives us a value of negative 11 point 35 and we have a 0.145 mess and a 50. It&#x27;s a positive 50 sign because it&#x27;s going up. It&#x27;s a positive fifties side of 40 minus zero, since it did not have an initial velocity in the wind direction, so that gives us a initial. It gives us a change of momentum in the UAE direction off 4.66 And because thes are vectors, you can figure in there, um, these two values to get my impulse of 12.26

Sri Datta Vikas Buchemmavari · Answer

in this problem. We have a ball that is initially moving with the velocity off 50 interpret second and has a massive cedar 0.145 kilograms. And after the ball hits the back, it is moving with the velocity ofsixty five meters once again at an angle of 30 degrees with the horizontal. Let&#x27;s say, as usual, our daughter is our X axis and vertical. Either way, access. We want to find out the impulse components in both X and y directions. You can simply do this because we know that impulse is the change in the window. Hence, and that is final minus B initially, nor the victor signs on all of the all of the symbols here. That&#x27;s because we have a two dimensional problem with Dr Conference in exact directions. Now we can apply this equation in both X and Y directions and find out the impulse confidence now for the impulse next election. That would be the final moment of the next election, minus the initial on the next election, which is now in the final case. When you have 65 meters per second, we can divide the velocity into two components because this is 65 meters per second. I&#x27;m X angle of 30 degrees. We have ah x and Y company. The ex confident is 65 cost 30 that as the compliment is 65 Scientist E. But I also know that this the ex confident of director is in the left or direction, which means the ex con parent is actually negative. Now our final momentum in the ex competent is mass. You should see the 11 for five kilograms multiplied by the velocity which is minus 65 Bastardi minus The initial wanted was simply the mass times velocity because the velocity is complete in the ex direction which is still a 1145 times 50. This turns out to be 15.41 kejian meter per second. If you put it into a calculator Now for the white confident we have again bf why defining moment in the white direction minus he i y the initial order in the white direction. But the mission went up in the white direction is zero because I&#x27;ve always moving horizontally. Hence it is simply the final moment of in my direction, which is mass. They want 145 times the vertical component of the velocity It is 65 signed 30. There were the Scientology zero cost 30 is through three. By do, this turns out to be 4.71 kilogram meters per second. Also in order, there is a minus. And here I&#x27;m sorry, forgot to write it down because our impulse is in the left for direction. And this is positive because our impulses in the coordination the compliment that seems reasonable. Because if a ball came in horizontally and then left at an angle, we&#x27;re expected to have a we&#x27;ll expect the force to be somewhere in between. Now, for part B, we want to find out the force components if the time period for which is they&#x27;ve fourth, did I, period for which the force has is killing in the problem. The time period is giving us 1.1 fire millisecond, which is 1.75 to 10 for minus three seconds. And hence they&#x27;re forcing the ex conference is simply the impulse in the ex component directed by earlier because we know involved is force times that I&#x27;m pretty and they spread disease bacteria question into confidence and for the ex confident we have this and for the wine confident we have, I&#x27;ve I&#x27;ve identity. Hence, FBI is simply 0.471 I&#x27;m sorry for 171 which is why you want a bite daddy, which is 1.75 in due time four minus three seconds. Which turns out to be 2,690 unions. Nor that I rounded it down to three. Significant beat it. Similarly, effects is minus 15.41 divided by 1.75 into 10. For industry which is minus 8,800 mutants, these are forced confidence.

Paul A. · Answer

once again welcome to a new problem at this time will given a baseball that has a mass. So this is This is the information that&#x27;s given. We have a baseball with the mask off zero point one four five kilograms, and it&#x27;s moving towards the right with an initial velocity, which happens to be, you know, going to say positive forty five minutes per second because it was the right is positive. Um, so that&#x27;s the peach. That&#x27;s the baseball peach, and it&#x27;s going to move all the way up until a specific point where there&#x27;s a bat, um, and the the batted ball. So this is the Peach ball, and this is the Barton Bowl. So the bartered bowl happens to have a final, which we&#x27;re going to call the final velocity off negative fifty five meters to second. So that&#x27;s what we&#x27;re given S O in part A. We want to find the change in momentum. Okay, we want to find the change in momentum. That&#x27;s the magnitude of the magnitude off the change in momentum and the impulse Lenny in Part B. We want to find the average force, the average force that&#x27;s responsible for that specific change in momentum. So that&#x27;s what we&#x27;re looking for. S o, you know, starting on part, eh? We see that to get the change in momentum. It&#x27;s just the final of the final momentum, minus the initial momentum. Remember, momentum is the product off the mass and Exxon under velocity. So it&#x27;s just m of the final minus V initial, which is m. The final happens to be negative. Fifty five meters per second minus V Initial is positive forty five minutes per second and so way have to plug in the mass. The mass happens to be zero point one for five kilograms, so zero point one four five kilograms. And so if you do the math, you end up getting a change in momentum off negative fourteen point five kilogram meters per second. The highlight off this is that the magnitude off the change in momentum happens to be fourteen point five kilogram meters per second. So that&#x27;s just the fast part. You know, want to find the magnitude You can recall that the second part and we&#x27;ll do that on the page. Are you interested in finding the the impulse, the impulse? Remember impulse, which is J the vector sobs superscript on top of it. Defected line direction on top of it happens to be if they are really force times change in time. So this is, um that happens to be a our impulse. The well, we have to backtrack a little bit. That happens to be Howard. Change in momentum. Okay, so this is this happens to be our change in momentum and this is exactly the same as our imports. So you know, if if we take it, we&#x27;ll take the change in momentum and really mean compare that to to the to the problem. So if you go back, you find that the change in momentum was negative fourteen point five kilogram meters per second, a negative fourteen point five kilogram meters per second. So that happens to be to be our impulse. You know, this is the impulse And so the magnitude ofthe the impulse which I&#x27;ll just put the the absolute value sign to show that this is the magnitude of the impulse that happens to be equivalent to fourteen point five kilogram meters per second. You know, that&#x27;s the magnitude of the impulse in part B, which we can pick up in the next stage. We supposed to find the average force that&#x27;s required. I remember you know you had the budget ball right there on the time it takes for that contact happened is two point zero zero milliseconds, which we can change two seconds by multiplying by one second off a thousand milliseconds. And that gives us two times ten to the negative three seconds. That&#x27;s the time it takes to off contact between the bat on the ball. So we have the last e way because it goes in that direction so they have red force times. Delta t happens to be the impulse. And so the average force is the summers, the impulse of adult titty. Going back to the previous page, you can see that we are an impulse off negative fourteen point five kilogram kilogram meters. Second, I wanted to fight that, by the way, time it takes for that contact happened. And so our final average force F what you call F average calling average eyes going to be the same as seven, you know, roughly seven point two times ten to the three Newton. That&#x27;s our problem right there. I hope you enjoyed it Feel feet share really comments or questions? Um and, uh hope you have a wonderful day a Sze Yu up. Who are the problems? I want to see you soon. Okay, Thanks. Bye.

Zulfiqar Ali · Answer

but we have the most of the best ball. The mass of the best ball is equal to 0.145 kilogram. The biggest ball has speed off 45 point. You don&#x27;t meter per second, so the speed off bitch to ball is equal to 45 45.0 meters per second. The basketball has a speed of 55.7 meters per second, so the batted ball has a speed equal to 55.0 meters per second in the opposite direction and the time interval different. The ball in contact with the bed is a 2.0 millisecond, so Delta T is equal to 2.0 milli second. Well, we know that it momentum is given by mass times velocity and total. Ford&#x27;s F is equal to the Tu minus B one divided by a Delta T. Well, let&#x27;s call this equation number one and this be acquitted. Number two Well, in both momentum to room. Ah, see his feet, uh, in both is equal. Do are changing momentum and change in momentum is final momentum minus initial momentum. Okay, now let&#x27;s do bark A No, we departed a Let me crawl down. Yes. So here we do park here. Well, first we take the batted balls. Lost is the final velocity and it&#x27;s directions. The positive direction and we take the pitched balls we lost is the initial velocity. And so it&#x27;s direction will be the negative direction Eso we have Ah re I is equal to minus 45.0 meters per second and Rieff is equal. Do 55 find zero meter or second are we plug our values for M and initial speed into question number one. So we get the initial momentum off the ball. So initial momentum of the ball is equal to 0.1 for five, uh into minus of 45.0 meter per second on that is equal to minus 6.525 minus 6.5 um 25 You look around me too, per second, right. And similarly, a B two is equal to 0.145 into 55. Find zero. That is equal to 7.975 You look around May 2 per second. It&#x27;s meter per second, right on the change in momentum. Delta p is equal to be to minus, uh, be one. Well, B two is 7.975 minus into B one. Well, that is minus 6.5 to 5. And therefore change in momentum. Change in momentum is equal to 14.5 our Gilo Kromm meter per second. Okay, All right. And also, we know it in bolts is equal to change in momentum. So impulses able to change in momentum. Therefore, impulse physical too. 14.5. Lucky Luke Graham meter for a second, right? Okay, No, let&#x27;s do part B. Well, we want to find out on the total force. Well, the total force is equal to 7.975 minus into minus 6.5 to 5. Divided by do 0.0 times 10 to the power minus three. So total force is equal to 7000. About 250 Newton

Paul A. · Answer

once again welcome to a new problem. Uh, well, given a ball that&#x27;s traveling. So this is the information that&#x27;s given. So we have a ball that&#x27;s traveling towards the right. The posed to the last e over forty a. Meet us for a second. That&#x27;s the bull traveling towards the right, and then it comes into contact with the back. Okay? And once it comes into contact with the bat, it takes off upwards. I got an angle off thirty degrees. So this is the information that&#x27;s given the mass of the ball. Happens to be zero point one four five kilograms on the time it takes for the ball. To have contact with the bat is one point seven five milliseconds, which we can change right away two seconds by multiplying by a reciprocal of a thousand. And that&#x27;s going to give us, you know, one point seven five times, ten to the negative, three seconds. So that&#x27;s how much time the ball and a bad eye contact. Remember, The ball is coming from the left, moving toward the right, and then it gets hit gets. He had such that it&#x27;s gonna have component velocity. So, you know, this. It has a velocity in the horizontal direction. Okay, which you can call the final X. And it also has the final, uh, why this one is the initial lost its in the ax off the initial in the X is for e and then V initials in the white happens to zero because of all is not going up or down. So that&#x27;s the information we were given. I was supposed to find the once to find the horizontal. So this is the average force we have want to find the horizontal component. They are real force and we also want to find the vertical component off the average force. So, you know, we&#x27;re calling it the average acts and then the average y. So looking at this problem, you always have to think about the bald in terms ofthe X and y. So the faster we&#x27;re going to do is to compute the initial momentum. This happens, you know, when the ball is moving towards the right, V initial in the ex happens to be forty meters per second. So the initial momentum in the ex is the mass off the ball times the initial velocity in the X. The Marcel&#x27;s bo happens to be zero point one four five kilograms and the initial velocity in the X, which is in the positive direction, is positive forty meters per second. And so, if you plug in those numbers, you get that. The initial momentum in the X is five point eight kilograms leaders per second. That&#x27;s the initial momentum in Ex. Remember, our target is to get there the vertical and the horizontal components off the average force. So if you think of it in terms of the diagram, you know what you&#x27;re saying is that you have you have, you know, once the ball moves this way and then there&#x27;s a bad the body heats the ball that way. And so these Air Force is an average force that&#x27;s responsible for that within a specific time. That average force has two components, says the ex component, and it also has the white component. So that&#x27;s what we&#x27;re trying to get. So we always have to think about the X and Y and this problem. But everything starts with the initial stuff. So this is the initial momentum in the X. Remember the ball troubles up until it comes to to the back. Okay, so when he hits the back, it&#x27;s going to go up that way. So there are two components. The negative velocity, the negative final lost in X on the also the positive final velocity in the wide because it&#x27;s going out. But if you look at the problem, the telling us you know that this ball it&#x27;s traveling output. So if we want to get the the final momentum, the final momentum in the X uh, we&#x27;LL need to find we&#x27;ll need to take the mass times the final velocity in the eggs which is going to be negative because it&#x27;s pointing in the opposite direction on DH. So this is this. This is now where you used trigonometry. Remember this angle here eyes thirty degrees. Okay, we can even call it data for purposes of explanations. And then this&#x27;s the last Eve actor. This is a final velocity. This is the final glass in the attic, so you can see using trigonometry. The final velocity in the X over the final velocity is the same as co sign off off data. So that means the final velocity in the X has to be the final last e times cause I&#x27;ll data, but it&#x27;s in that direction. So this is gonna be negative. Final velocity data. So simplifying this problem, we have m times the final lost in the X which is negative v final co sign off Daddy on DH. Then this changes to plug in the numbers zero point one four five kilograms. That&#x27;s the mass times negative. The final velocity. As you can recall, if you go back, the final velocity was given us way have to check. He was given us fifty two meters to second. So don&#x27;t forget about the final lost this final blows to right here It happens to the VI final equals two fifty two meters per second. So going back, that&#x27;s the number we&#x27;re gonna plug into the formula. So I remember there&#x27;s a native fifty two meters per second time&#x27;s coastline off thirty. Okay, Time&#x27;s co sign off, Daddy, all we can see the whole thing a cz a unit. So we have the meters per second at the end because so gonna have a meters per second at the end. So this times co sign off off early meters per second if you multiply those two numbers, you get negative. Negative twelve. Sorry, you get negative. Six point five the read kilogram meters per second kilogram. Meters per second. So you know we have we have two things Critical pieces of information that we&#x27;ve picked up so far. You know, we have this baseball that baseball that&#x27;s going up was hit by a bad. We have the initial final lost in the ex. We also have finally lost in the UAE. We&#x27;ve computed the initial momentum, the initial momentum in the X Going back on this page, you can see that the initial momentum in the axe happens to be this one right here, five point eight kilogram meters per second. That&#x27;s positive. And then we also have the final moment of in the X. If you go back, happens to be negative six point five three kilogram meters per second with six point five three kilogram meters per second. So the impulse J, which is equivalent to the change in momentum, is the final momentum. This should be a final, the final moment, um minus initial momentum, which is the same as negative six point five three kilogram meters per second minus five point eight kilogram meters per second on DH. That&#x27;s going to give us remember, this is a process that&#x27;s going to help us get the final, get the average average the last. If you put in those two numbers, you get negative twelve points, three three kilogram meters per second and so this&#x27;s very helpful piece of information. We need the force. Another thing that happens is when when baseball gets he liked that it&#x27;s being hit by a specific force that force us to components thie f the horizontal component which is negative, and the vertical component which is positive. We&#x27;re the position to find the horizontal component, which is the same as, um the impulse in the X over the change in time. Remember, the change in time from the beginning was one point seven five time Stand to the negative three. So this is the same as negative twelve point three three kilogram meters. Second off, one point seven five times, ten to the negative. Three seconds. Andi, this is going to give us final answer for the horizontal force. Vexes Simmons negative on seventy fifty Newton. You know, approximately that&#x27;s the average of this is the average force in the horizontal. That&#x27;s the average, forcing the horizontal average force in the horizontal in the next spade. We want to repeat the process so that we can get the same information this time for the white component. Remember, the ball is moving that with the initial velocity in the axe, happens to be forty medias per second, as you can recall. And then also, uh, now we&#x27;re kind of like focusing on the wire component, but but still, you know, this is helpful piece of pieces of information initially lost in the X forty meters per second. Initial velocity in the UAE happens to zero meters per second because it&#x27;s not moving up and down the ball gets to ah, baseball bat gets heat like that and so it has a final velocity negative final velocity in the X and then it also has a legally final velocity in the UAE again will focus in on the white components, wantto find the initial momentum in the UAE. The initial momentum in the wife happens to be the mass of the ball times the initial velocity in the y. So this is zero point one four five kilogram times zero meters per second on that just gives us a momentum of zero kilogram meters per second in the wind direction. The other thing that happens is you know, once the ball is here, uh, we want to find the final momentum in the wire. And that&#x27;s just the mass times the final velocity in the white direction. It happens to be positive because, uh Portis positive. So this is zero point one four five kilograms times the final velocity in the wife positive again. You know, going back to our small diagram. You could recall if this is Ada and this is the final and this is the final. And why you can see that the final the Y has to be the final time. Sign off data. Okay, so then this is this is what we&#x27;re gonna plug in right there. The final was if you can call fifty two meters per second and then time sign off data, which is study on this is Matus per second. That gives us momentum in the UAE, which is three point seven seven kilogram media&#x27;s for second. And so now we can get the the impulse in the wife, which is the final momentum in the Y minus initial momentum in the UAE. And that gives us the final moment on this three point seven seven kilogram meters. Second, remember the initial momentum in the Y. Zero kilograms meters a second. Ah, And so now we have all the information we need to find out what force in the why we go to the next page. And you can see that if we have that this would be f this thie f y. And this would be a negative f x. So we&#x27;re interested in finding that s o the final force Average force. This is an average force, the final average force, or the average force in the white direction eyes the same US momentum in the white direction off the change in time. And we just found that the momentum in the white direction is three point seven seven kilogram meters per second. And then we divide that by changing time changing time. We got that from the beginning which is one point seven five times ten to the negative three. So this is one point seven five times stand the negative three seconds and So, you know, if you plug in the numbers, you get that for the Y direction you&#x27;re going to end up with a twenty one fifty Newton&#x27;s. That&#x27;s the coverage force in the wind direction. Our thanks fortune. The video, just to kind of like summarize, wanted to find the average force in the ex direction, which happens to be negative seventy fifty mutants and the average force in the white direction, which happens to be twenty one fifty mutants. The key is to break up the final momentum into two components. The wind, the X and also the initial momentum into two components. The wind, the excellent to use the impulse to get the average force. Remember, the F times Delta T, which is, the impulse is, is helps us get the force because you solve for for F so Africa. Lt&#x27;s too, the impulse off of the change in type. Thanks for watching and have a wonderful day

Problem

Object 1 travels with an initial speed of $v_{0}$…

Problem 24 Easy Difficulty

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