at-the-intersection-of-texas-avenue-and-university-drive-a-yellow-subcompact-car-with-mass-950-kg-tr

Question

At the intersection of Texas Avenue and University Drive, a yellow subcompact car with mass 950 kg traveling east on University collides with a red pickup truck with mass 1900 kg that is traveling north
on Texas and has run a red light ($	extbf{Fig. E8.41}$). The two vehicles stick together as a result of the collision, and the wreckage slides at 16.0 m/s in the direction 24.0$^\circ$ east of north. Calculate the speed of each vehicle before the collision. The collision occurs during a heavy rainstorm; ignore friction forces between the vehicles and the wet road.

Ben Nicholson · Accepted Answer

problem. 8.41. We have a collision between a yellow subcompact car and a red pickup truck which will call A and B, respectively. They were initially moving well. The the compact car was initially moving east. Pickup truck was originally moving north and then they collide and stick together and move off at 16 meters per 2nd 24 degrees east of north. And since we&#x27;re calling this X in this why, it&#x27;s worth noting that this angle is measured from the positive. Why direction? And so, whereas we&#x27;d normally expect to have a co sign for the X component of this, for example, we&#x27;re actually going to use the sign because it&#x27;s 90 degrees minus. This is 90 degrees minus this ankle. So we know that the white component for this one is zero initially. Similarly, the X component for this 10 initially, then from this and then being careful with using sign for X and co sign for why we know that or we can readily compute that. The X component of the final velocity is six and 1/2 meters per second, and the white components is 14.6 meters per second And now this is a pretty simple exercise in the conservation of momentum because we know that the initial velocity velocities of either one have a zero. Why or x component? So we take the equation for the X component of the momentum. For example, the contribution from the pickup truck is going to be zero. So we just have the mass of the compact car. Time&#x27;s what we would like to know about it eggs and this is going to be equal to masses of the cars because they&#x27;re stuck together times the x component of the final velocity. So the initial speed of the compact car Yeah, and so we can see that sister just at me plus m b divided by name, times the X component of the final velocity, both of them together. And this ends up big 19 and 1/2. You just for a second and pretty much the same story again with white component of momentum. Except now we&#x27;re learning about. But the truck was originally doing and we need the white component of the final velocity. Some of the masses divided by now the massive truck like final speed loss to be sorry. And then putting the numbers in for this one, we find out that it was going 21 points. Oh, I&#x27;m sorry. I should also have noted this the compact subcompact car at a massive 50 kilograms like nine. And the pickup truck has a mess. 1900 killer. Otherwise, it will not be clear where these numbers came from. All right, So that&#x27;s how you figured out when you have an elastic collision and you know, the initial directions have either one or both of you. You could be told what the final outcome in terms of the velocity waas backwards, Figure out how fast

Ben Nicholson · Answer

problem. 8.77. We have two cars a Savannah, a traveling to the South and this SUV be traveling to the West. The masses were given here. They run into each other as cars do and slide together for some distance it along the ground. Now we&#x27;re told the distance which they slid before together before stopping and given the X and Y components of that displacement. We&#x27;re told what the coefficient of kinetic friction is between the come combined cars and the ground. And then what we want to do is figure out what we&#x27;re the what were the speeds of the cars before they had the collusion. So this is going to have two steps. First, we&#x27;re going to be thinking about energy, and in the second we&#x27;re going to be thinking about momento. It&#x27;s a little bit of preliminary here. Um, we want to know what he is. That&#x27;s easy. We just use the Pythagorean here, um, so is equal to eight points 39 heaters, and we&#x27;d also like to know what state it is. Data is the arc tangent of the opposite over Jason sides, and this is about 50 degrees, so little Roman numeral one here. We know that in order to be sliding in the first place, the combined car object had to have some kinetic energy. Will call m a plus envy began and their speed right after they started citing will be just be. And now, in order for this to it stopped some amount of work had to have been done on it. Two You know, it is a kinetic energy. That work was done by friction. So we know the work is the force times the distance over which the forces exerted? No. Then the force of friction is the coefficient of friction. Friends, the normal force which this is. Just wait big anti Miss Jean and then the distance we called the So the speed they&#x27;re going immediately after the collision is the square root of two coefficient affection, the acceleration of gravity times this distance. They were going 11 0.1 meters per second together right after they hit. Now, in order to use this for the conservation of momentum because it is a vector, we&#x27;re going to take advantage of the fact we know the initial velocity of a was entirely in the wind direction and the initial velocity of B was entirely in the extraction in order to make our lives easier. This conservation of momentum calculations or are in fact, we need more information we wouldn&#x27;t have if we didn&#x27;t know what the directions of you are already. So let&#x27;s turn our be into a vector before turning our attention to momentum, all we could think of this is the first part of turning our attention for momentum. So this is going to be the magnitude of this and the coastline of the angle the unit vector in the extraction sine of the angle unit vector in the wider erection. And just so we don&#x27;t have much negative signs that we don&#x27;t really need, Uh, well, that left b positive extraction and down the positive direction. So you work this out and you find that the velocity vector immediately after the collision, the 7.14 you just for a second and X and 8.5 meters per second and why? Okay, so now the momentum of the combined cars together is the sum of them answers I&#x27;m a philosophy just found, and the momento from a will be its mass times its speed times the unit vector in the direction it was going and similarly, for and not just breaking this apart. We&#x27;ll find the d A is equal to Big M over and a I miss the white component our velocity here and this works out to be 21 meters per second. The speed of the SUV has the same sort of form to the equation because there&#x27;s nothing special about one or the other in terms of the physics involved. Maybe one of them had a nicer color on the other. There&#x27;s no way crust No, this was going 12 meters per second. So perhaps the SUV was slowing down and trying not to run a red light and didn&#x27;t do it in Time Sedan or yeah, who knows what we&#x27;re not told? But in any event, these air how fast they were going before the collision, and, uh, we worked backwards. Um, what? The results were what the initial conditions were

Eric Mockensturm · Answer

and this problem. We have a car traveling south in a car traveling east and they collide. The car traveling south has a mass of 1180 kilograms and a speed of 24 meters per second. I made an axis here so that east and north are positive. So that&#x27;s why this velocity is negative because he&#x27;s traveling south and the other car has a mass of 2000 foreigners 70 kilograms and it is traveling east at 16 meters per second and we want to figure out what happens when these cars collide in the stick together. Now we expect that we get off the last e vector somewhere down and here because one car is going south and one is going in. So we expect something down here so we can use conservation of momentum in the why and the ex directions. Because if we look at the two cars as a entire system, then there is no external impulse in in these directions acting on the cars, so momentum will be conserved. So the original momentum in the Y direction or in the north direction is M one V one y, and then afterwards It&#x27;s the total mass of the two cars and the new velocity in the Y direction and likewise in the X direction. Because the first car has no over lost in the X direction it the momentum is completely that of the second car or second vehicle. And then the momentum afterwards is the total mass of two vehicles and a velocity in the X direction we can then solve. Obviously, in this equation we know everything but the three. Why? And here we know everything except for three X so we can solve these. And we find that V three y is minus 7.76 meters per second again. So that means that the two cars are going to wind up going south. I&#x27;m as we expected, and the X 33 x is 10.83 meters per second. So again they&#x27;ll be going east as expected. So somewhere southeast now, to get the magnitude and direction. Obviously, this this is plenty of information to, um to define the vector, the velocity vector, you know, both components. But if we wanted in magnitude and direction, we find the magnitude by taking the square with the sum of the squares of the components and that winds up being 13.3 meters per second. And then if we measured, they&#x27;d at this way. We know we have 7.76 velocity meters per second in this direction and 10.83 in that direction. So we could take the tangent of that angle to Canton of that ratio or the universe tension of that ratio and that gives us 35.6 degrees, so this factor is 35.6 degrees south of

Dading Chen · Answer

Okay, so for this question wins a separate to two parts. So let&#x27;s take a look at the X direction first. So according to conservation law, fomenting the additional momentum along the X direction should be go to the final moments along the X direction. So therefore have m one. You are X plus m two V two x plus M three with reacts is M one plus M two plus M three times we have X. So M one here is the mass for the truck and we want acts. Here is the s component of initial lost you for that truck. M Who here is the mess hall A car and veto acts. Here is the components of the initial lost people A car m three here is the mass for miss eyes and ah, we three acts Here is the X component of initial velocity for the midsize car and the final one hand should be It was, um, on plus m two plus m three times with the Apax, which is the total mass off the three vehicles times toe. Ask him one of the final speed. Okay, because it&#x27;s a head on collision. So eventually they will stick with a shocker. And we to actually your should be was your meter per second OK? Because he was traveling through North. Nothing&#x27;s he doesn&#x27;t have any ask components along the X axis, so I z zero. So we know the we have acts Comey expressed as VF Corp Santa. Okay, so now you can plug in bed. So the question they will have simply m one of your ax plus employees read. Reacts is M one plus M two plus M three as we have Cassandra. So therefore, we, of course, and figure this evil. Everyone relax, plus temporary with reacts over and one plus two plus in three. So we know the mass for the truck is 2100 kilograms and a mass for the car is 1200 field brands. The Maxwell midsize car is 1500 killed, right, and the X component of the initial velocity for the 1st 1 is two meters per second, which is the initial velocity for the truck in the initial last E for, uh, missiles, car is 10 minute per second. Now can plug in bed, so the equation to determine where we have course and data. So we asked. Oh, sorry. So we have something I should be able to. Um And while we want acts which is 21 100 kilogram times to a 0.0 meter per second, plus 1500 kilograms times 10 meters per second over a total mass of three were goes which is 2100 kilograms plus the 1200 kilograms plus 1500 kilograms. And this will give us we have course I intake, which is the X components of the final speed, is actually equal to sorry for meter for a second for next. Wise Ah, the momentum along the y direction. And he also a baby conservation law. Momentum, Which means that unusual moment on a white directions. So vehicles with the final moment along the right direction would you have someone we want? Y plus eventual return. Why bust em three really wise. He could anyone past him to bust em. Three tests we have. Why so for this question, we want why we through watching you go zero meters per second, which is the white components. But a initial velocity off the truck and the white combines But initial last day off their midsize car. The reason why both went equals zero is because both of them were traveling toward East, so they don&#x27;t have any white components along the Y axis. So the workable for both initial blasting tribunal zero and we know B F y, which is the why component for the final speed should be, will be have signed data. So therefore, if you&#x27;re talking about silly question where just mpm to veto y is equal and one with us em to us entry has we have signed data. So we, too are here is the white components for the, uh, cars initial velocity, which is the initial lasting follow car since the car was traveling towards north. So if it was an arranged over here, where we have signed data is he will it will be, too. Why, over on one plus m to bust em three. So, uh, therefore, well, we know the the mass of the cars and the speed for the car. And now I can determine the why components off the final speed, which is every site data is just simply equal to 1200 you know where times 5.0 meter per second over Ah 2100 killer wears plus 1200 kilograms and then plus 1500 kilograms. And this will give us the white components for the virus. Bees bow 1.5 meters per second so they&#x27;re broken. Determine the final speak so the finest B is just simply equal to square root. We have close anteater Square, which is the X component of the final speed. Plus we have sank data Square, which is the y component of the final speech. And it&#x27;s looking plus square root 4.0 mirror per second squared plus 1.25 unit for second square which is equal to 4.19 meter per second now in determining the direction so that Iraq should be along several angles here. So that&#x27;s 2 10 years later. So we know tension data. Can we go to the white components off the finest be over the ass components off the finest be, which will give us 1.2 if I meter per second over four meters per second and this will give us tension thing up is equal to zero point 312 If I so therefore can determine angle here, which is the inverse tension function. And this would give us the angle. It&#x27;s about 17 uh, 0.35 degree. So if I drew a terrible you should look something that is so this is the positive X access, and they&#x27;re forcing his eyes positive. 17.35 degree. There was something of this. And this is the direction for the final speak. If we consider north, East, north, east, west and south, this is actually the direction receive. This is north of East. Okay, So eventually, three cars or three miracles will travel, uh, at an angle 17.35 degree at north of east, and, uh, he&#x27;s out answers for these questions.

Paul A. · Answer

This is an interesting problem. It&#x27;s a collision problems so well given well given on intersection that&#x27;s running west east on one direction. And then, you know it&#x27;s running, you know, not self in another direction. We have two cars. Car, Eh? So this is what happens before. So car A with the mass off given the Marcel&#x27;s car, eh? It happens to be, um so you know, we&#x27;re gonna have to get the mass of this. So the mass ofthe car A happens to be two thousand kilograms. This is two thousand kilograms muscle car, and it&#x27;s moving in the X direction. So initial the velocity off here, the ex direction happens to be, you know, we don&#x27;t know what that initial velocities in the ex direction. We do know that the initial lost in the white direction his zero meters per second because it&#x27;s moving from West Teo east. So this is kind of like in the postive direction. You want to think of it that way. Then we have another car, will given cobby that&#x27;s moving. So car is moving west to east and then Kirby Mom is moving from north to sup. It&#x27;s moving from not this out so you can have conventions where not South can be negative. For example, if you want Andi, that&#x27;s just fine. You know, we could say, If you&#x27;re going downwards, that&#x27;s negative. If you&#x27;re going to the right, that&#x27;s positive. You&#x27;re going upwards. That&#x27;s positive. If you&#x27;re going to the left, that&#x27;s negative. Those are conventions you can use on DH, then the muscle. He happens to be given us fifteen hundred kilograms. The initial velocity off B in the ex direction happens to be zero because it&#x27;s not moving in the extra action. It&#x27;s moving not south, and then the final velocity, or rather, the initial velocity off being the wide direction. That&#x27;s kind of what&#x27;s given. Mom happens to be, if you if you say downwards his negative. So that&#x27;s going to be not South negative, fifteen meters per second. That&#x27;s the information we&#x27;ve given before, and then after afterwards, what&#x27;s gonna happen is the two cars will collide at the intersection, and B, this is a this is B and then they&#x27;re going to move a certain direction. So this is sixty five degrees. This is east. This is west. This is not who&#x27;s so so they&#x27;LL have a final Kamen Velocity, which you call the final and that vi final. Kamen Velocity has component factors, so the downward downward component vector would be the final sign of sixty five. As you can see, because it&#x27;s opposite the angle sixty five and then Cem VI final in the X direction will be the final. Of course, I knw of sixty five. So those are some things we&#x27;re given and we want to find out in part a. What&#x27;s the final? What&#x27;s this Final velocity combined velocity after they collide and then we also want to find out. But the initial velocity in the ex direction for a okay, velocity off he just before collusion assume we have limited friction and were using the laws ofthe conservation of momentum. So in party, the initial momentum because to the final momentum. And we want to find the initial velocity. So initial momentum in the acts will start with the ex direction. Use the ex direction to find the final velocity. So the initial momentum in the X it would be the Marcel&#x27;s eh times the initial lost you, eh? In the X plus the Marcel&#x27;s B times the initial velocity of be in the X. When they stick together, their masses combined as a son and they have a common velocity in the X, which happens to be the final sign of sixty five. This is this is what we&#x27;re looking for. The V finer. So you could see the VI final is equivalent to the Marcel&#x27;s, eh? Velocity of pay. The ex plus Marcel&#x27;s b lost your being the ex all over mass of a plus Must will be a sign of sixty five is going to be sign of sixty five with plug in the numbers Get to see that the muscles, eh? Going back is two thousand kilograms two thousand kilograms and then the velocity of pain The X is Come on You were using lost you so massive Massive Hey, um maybe we should use why for this one. So two thousand kilograms? Ah, mussels. I&#x27;m sorry Way have to do in the white direction not the ex direction because we don&#x27;t have the initial blast e both home. We don&#x27;t have the initial blast. You off off, B No, we don&#x27;t have the initial velocity of a couldn&#x27;t see. We don&#x27;t have this one. So we have to go back and do it in the white direction. So was saying initial velocity in the wind direction. So this is not expert. We are going to do. Why then? And of course, it makes sense for the y to be signed. You could see that so that why sign? That&#x27;s That&#x27;s what I&#x27;m going to use. We just don&#x27;t have the sub scripts for for why, right here to change that. So initial velocity off in the y. So this is not the ex direction, but this is the wind direction. Just recall. So this is why this is why this is sign of sixty five on then Also we have initial blast. Why initial velocity? Why will be so This is two thousand kilogram initial last year off in the white direction is zero meters per second showed. You know, that&#x27;s that&#x27;s how we&#x27;re doing this one. And then we added to the mass off B which happens to be fifteen hundred kilograms and forget the killer blond right there. Fifteen hundred kilograms times the initial velocity off be in the white direction and that happens to be negative fifteen meters per second and the negative sign touches houses just come in the direction. You know what what direction is? And then the muscles, eh? Two thousand kilograms, plus the muscle B, which is no, which is fifteen hundred kilograms. Okay, men, Time sign of sixty five. And so something you want to know is that Oh, when you plug in, the numbers will be able to get the of the final, which happens to be seventy. We&#x27;re not seventy, but seven seven point one meters per second. This is the final seven point one meters per second. Um, sign this case. The reason why in fact, we don&#x27;t even have to use the minus of this minus. We don&#x27;t have to use this minus right here. You were comfortable. We just know the direction. Let&#x27;s think about the direction East west, not south. So you don&#x27;t have to use those sciences We&#x27;ve done right. Who left before eso coming back to see that the final velocity is seven point one meters per second and then the second part of the problem Oh, you want to find I want to find the initial velocity if you call it this one right here. Initial velocity of a That&#x27;s what we want to find that one V eh? I x So we want to find the initial velocity off a which we&#x27;re calling the A i X. So we&#x27;re going to use the ex direction formula Now We&#x27;re dealing with ex direction and had so little saying the initial momentum in the X here used initial momentum in the white direction just to be clear about that now it was saying initial momentum in the ex direction because to the final momentum in the ex direction, initial momentum in the ex direction is muscle times, velocity of a initial velocity of paying the ex direction. Plus must be time&#x27;s initial velocity of B in the X direction. When they stick together, we have Marcel&#x27;s hate plus must be But now we&#x27;re dealing with the ex direction on this side. You see, we had I had lost why and then this one was was our If you go back to the diagram the final sign sixty five you know that you could call that V off f y And then this one is a vey off f of X. So we&#x27;re going to use V o F of X, which is the call sign off sixty five. The call sign of sixty five. I already have V from the previous problem. Would you call the final right here? That&#x27;s Avi file. Eso won good ship. Want to solve for the initial velocity of aid X direction No one was simplified. That problem. We get initial velocity of pained extractions. Emmy plus M b. The final co signed sixty five and then minus empty, be initial in the X all over the muscle. He plug in the numbers Marcel Hayes two thousand kilograms. So we have two thousand kilogrammes times. We&#x27;LL run the plus one thousand five hundred kilograms times seven point one meters second co sign sixty five minus muscle B is, um one thousand five hundred kilograms. But remember, the initial velocity of being the ex direction happens to be zero. So that&#x27;s just means that we&#x27;re not gonna have any momentum. In that instance, we have to divide all that bye the muscle a day, which happens to be two thousand kilograms. When you simplify that problem, you end up getting but the last e to be five point two five meters per second So this is the last year of a the ex direction. Come happens to be five point two five meters per second. Initial velocity of ain&#x27;t extraction Hope you enjoy the problem. We had to find the VI final Blast e when they meet in the intersection and they collide. And that&#x27;s number we had. And then we also had to find the initial last year a just before the collision. Okay, So if you have any questions, feel free to send them my way and have a wonderful day. Okay, Thanks. Bye.

Keshav Singh · Answer

So for this problem, we will let TB the time that has elapsed since the first collision. No external forces in the X Y plane act on the system, consisting of Cause A, B and C during the impacts with one another. The mess end of the system moves that the velocity it had before the collision. So if we said the original oh, we confined the initial mass center are not? Since we know a definition for the messenger to be, that&#x27;s some off the messes in me less MB. Let&#x27;s him see the massive because multiplied by the position off the mass center. The initial position. It&#x27;s not I plus why not? J and this is equal to the mass of Katatni times. Its position, which is zero bless the mess off Kabi and its position results is, you know yes, the massive cost c times its initial position rates position xy Since I yes, it&#x27;s why component twic times the ineffective J. And so from here we can solve for X bar, not the initial position off the messenger to be 0.3 exceed, So we&#x27;re just equating like components. And this is 0.3 times 32 feet Answer. Get X by not to be nine 0.6 feet. Similarly, for why Bar note the initial position of the messenger and the white direction is 0.3 times Y c that 0.3 tens 10 ft and we get them wine by notes. This city feet. So now we have the initial position off the mass Ente. So the position of the mass center before the collision, the velocity of the mass center we can create as follows. So using the Momenta, I am a plus m b bless M C times the velocity off the System V bar with the velocity of the mess center is equal to the some off the products off the masses and the velocities. So maybe a less and be maybe bless him. See V c. And so if we rearrange this, we confined the velocity of the mass center. We&#x27;re just label this as the velocity off the mess center. So we calculate the position of the mass center initially. Now we have the velocity of the mass center to simply be zero point 37 5. The a last zero point 32 5 VB plus 0.3 the scene. So no, we can calculate the point at which the cause hit the pole. So the cars that have collided hit the pole at point R P so they combine and hit the ball together. And this point R p has coordinates XP multiplied by unit victor I plus Y p much of black by j So we resolving this into its X and Y components. So XP times I plus why p times I, which is essentially the coordinates off the pole. You know, X Y plane is equal to the initial position off the center off mess eggs. Not I bless. Why not Jay? And since then, no external forces acting. It&#x27;s the velocity of the center of mess v times Time t so that will give us the position off the pole. So if we resolve he x components and white components, we get the following. So resolving the i components, we get that the X coordinate off the Pole XP physical. The X bar not plus zero point 37 5 v a Times T p minus 0.3 The sea times TP and TP is the time that has elapsed when the cars collided with the pole. Similarly, the Y coordinate is equal to why Bob Not Yes. So we equating to the sexually Jay on that I, my Pete and Jason grating B J components we get. Why bar not plus zero points the 25 times the velocity of B but a glide by TP So we have two equations here and believe that enable them one and to So we reached actually calculated XP. And why P Now what we do know is that 2.4 seconds elapsed when all three cars collided the pole. So therefore so you can say TP is equal to two point for seconds. And if we substitute T P is equal to 2.4 seconds into the expression above, knowing that we have the velocities. So we have the given velocities which will write down first. That&#x27;s right down our velocities. The A is given as 75 miles an hour, so we need to just convert this before we can use it. And that&#x27;s in the eye direction. So we need to convert this defeat a second so that we can use it now. Equation so 75 miles an hour is equal to 110 heat, the second in the eye direction. The velocity of Karbi is equal to 45 miles an hour in the J direction, and this is 66 feet per second in that direction. And finally, the velocity for Kasey is given at 60 miles an hour in the eye direction. And so that&#x27;s 88 feet, the second terms basis. Vector I. So now we have our time tp, and we hope to have our speeds off Car A, B and C the velocities so we can substrate them back into equations one and two since we know X by not and why, Bob. So yes, we have vectors for the velocity of each car. We have the initial lost year percent off mess off the system, and that&#x27;s it&#x27;s not. And why not? And we have the time tp So from Equation one, we can calculate the X coordinate of the Pole XP, and that&#x27;s 9.6. So he subject values in here plus 0.375 times 110 ft per second times Time T 2.4 seconds minus 0.3 and 88 times 2.4 when we get the X coordinate at P to be 45 0.240 Similarly in equation, too, we confined Y p and why P is three. Class zero 0.3 to 5. Time 66 tends to 0.4, and hence we get the white corn mint off the pole to be 54 point for eight, and that&#x27;s and feet. So we end up with the coordinates of the pole R P to be 45 0.2 ft and 54 point 5 ft.

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