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Collision at an Intersection A 1,550 kg car traveling east with a speed of 28.1 m/s collides at an intersection with a 2,550 kg truck traveling north at a speed of 20.3 m/s as shown in the figure. Find the direction and magnitude of the velocity of the wreckage after the collision, assuming the vehicles stick together after the collision.

Collision at an Intersection A 1,550 kg car traveling east with a speed of 28.1 m/s collides at an intersection with a 2,550 kg truck traveling north at a speed of 20.3 m/s as shown in the figure. Find the direction and magnitude of the velocity of the wreckage after the collision, assuming the vehicles stick together after the collision.

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
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Collision at an Intersection A 1,550 kg car traveling east with a speed of 28.1 m/s collides at an intersection with a 2,550 kg truck traveling north at a speed of 20.3 m/s as shown in the figure. Find the direction and magnitude of the velocity of the wreckage after the collision, assuming the vehicles stick together after the collision. SOLUTION Conceptualize The figure should help you conceptualize the situation before and after the collision. Let us choose east to be along the positive x-direction and north to be along the positive y-direction. In what direction is the blue car moving initially? O to the north O to the south O to the east O to the west Categorize Because we consider moments immediately before and immediately after the collision as defining our time interval, we ignore the small effects that friction would have on the wheels of the vehicles and model the two vehicles as an isolated system in terms of momentum. We also ignore the vehicles' sizes and model them as particles. The collision is perfectly -Select- because the car and the truck stick together after the collision. Analyze Before the collision, the only object having momentum in the x-direction is the -Select- . Therefore, the magnitude of the total initial momentum of the system (car plus truck) in the x-direction is that of only the car. Similarly, the total initial momentum of the system in the y-direction is that of the --Select-- an angle 8 with respect to the x-axis with speed v, | . After the collision, let us assume the wreckage moves at (For the next three answers, use the following as necessary: m,, m,, V, and 0. Do not substitute numerical values; use variables only.) Apply the isolated system model for momentum in the x-direction: (1) m,v - (m, + m2) Apply the isolated system model for momentum in the y-direction: Ap, = 0-EPy =P (2) m,v2 V, sin e Divide Equation (2) by Equation (1): m,v Solve for e (in degrees counterclockwise from the +x-axis) and substitute numerical values: 0 = tan" ° counterclockwise from the +x-axis Use Equation (2) to find the value of v, and substitute numerical values (Enter the magnitude in m/s.): m/s (m, + m2)sin e Finalize Notice that the final speed of the combination is less than the initial speeds of the two cars. This result is consistent with the kinetic energy of the system being reduced in an inelastic collision. It might help if you draw the momentum vectors of each vehicle before the collision and the two vehicles together after the collision. EXERCISE The eastbound car in the example is driven by an off-duty police officer, who knows her speed was exactly 20.0 m/s. From studying the angle e (and the mass of the two vehicles), she concluded that the truck was over the speed limit of 80 km/h driving on that secondary road. Of course, the truck also failed to stop before entering the main road. If the truck were not speeding, what should be the maximum angle for 0 (in degrees counterclockwise from the +x-axis) in this accident? Hint ° counterclockwise from the +x-axis Need Help? Read It Submit Answer
Transcribed Image Text:Collision at an Intersection A 1,550 kg car traveling east with a speed of 28.1 m/s collides at an intersection with a 2,550 kg truck traveling north at a speed of 20.3 m/s as shown in the figure. Find the direction and magnitude of the velocity of the wreckage after the collision, assuming the vehicles stick together after the collision. SOLUTION Conceptualize The figure should help you conceptualize the situation before and after the collision. Let us choose east to be along the positive x-direction and north to be along the positive y-direction. In what direction is the blue car moving initially? O to the north O to the south O to the east O to the west Categorize Because we consider moments immediately before and immediately after the collision as defining our time interval, we ignore the small effects that friction would have on the wheels of the vehicles and model the two vehicles as an isolated system in terms of momentum. We also ignore the vehicles' sizes and model them as particles. The collision is perfectly -Select- because the car and the truck stick together after the collision. Analyze Before the collision, the only object having momentum in the x-direction is the -Select- . Therefore, the magnitude of the total initial momentum of the system (car plus truck) in the x-direction is that of only the car. Similarly, the total initial momentum of the system in the y-direction is that of the --Select-- an angle 8 with respect to the x-axis with speed v, | . After the collision, let us assume the wreckage moves at (For the next three answers, use the following as necessary: m,, m,, V, and 0. Do not substitute numerical values; use variables only.) Apply the isolated system model for momentum in the x-direction: (1) m,v - (m, + m2) Apply the isolated system model for momentum in the y-direction: Ap, = 0-EPy =P (2) m,v2 V, sin e Divide Equation (2) by Equation (1): m,v Solve for e (in degrees counterclockwise from the +x-axis) and substitute numerical values: 0 = tan" ° counterclockwise from the +x-axis Use Equation (2) to find the value of v, and substitute numerical values (Enter the magnitude in m/s.): m/s (m, + m2)sin e Finalize Notice that the final speed of the combination is less than the initial speeds of the two cars. This result is consistent with the kinetic energy of the system being reduced in an inelastic collision. It might help if you draw the momentum vectors of each vehicle before the collision and the two vehicles together after the collision. EXERCISE The eastbound car in the example is driven by an off-duty police officer, who knows her speed was exactly 20.0 m/s. From studying the angle e (and the mass of the two vehicles), she concluded that the truck was over the speed limit of 80 km/h driving on that secondary road. Of course, the truck also failed to stop before entering the main road. If the truck were not speeding, what should be the maximum angle for 0 (in degrees counterclockwise from the +x-axis) in this accident? Hint ° counterclockwise from the +x-axis Need Help? Read It Submit Answer
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