At the intersection of Texas Avenue and University Drive, a yellow, subcompact c

Question

At the intersection of Texas Avenue and University Drive, a yellow, subcompact car with mass 850 kg traveling east on University collides with a maroon pickup truck with mass 1750 kg that is traveling north on Texas and ran a red light (Figure 1) . The two vehicles stick together as a result of the collision and, after the collision, the wreckage is sliding at 16.0 m/s in the direction 24.0east of north. The collision occurs during a heavy rainstorm; you can ignore friction forces between the vehicles and the wet road.

a.) Calculate the speed of the car before the collision.

b.) Calculate the speed of the truck before the collision.

Explanation / Answer

a)
Let east be +x axis

m1 = 850 kg

m2 = 1750 kg

let u1 and u2 are the speeds of m1 and m2 before the collision.

Apply conservation of momentum in x-direction

m1*u1 = (m1+m2)*v*sin(theta)

u1 = (m1+m2)*v*sin(theta)/m1

= (850 + 1750)*16*sin(24)/850

= 19.9 m/s

b)
Apply conservation of momentum in y-direction

m2*u2 = (m1+m2)*v*cos(theta)

u2 = (m1+m2)*v*cos(theta)/m2

= (850 + 1750)*16*cos(24)/1750

= 21.72 m/s

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