During the filming of a certain movie scene, the director wants a small car (mass 795 kg) traveling due east at 35.0 m/s to collide with a small truck (mass 3360 kg) traveling due north. The director also wants the collision to be arranged so that just afterward the interlocked vehicles travel straight toward the camera (which is placed at a safe distance, of course). If the line between the camera and the collision makes an angle of 37.0° with respect to north, at what speed should the trucker drive?

The trucker should drive at a speed of 11 m/s m/s

Explanation:

mass of the small car, m₁ = 795 kg

initial velocity of the small car, u₁ = 35 m/s (due east)

Mass of the truck, m₂ = 3360 kg

Initial velocity of the truck, u₂ = ?

Final velocity, V = u₁ sin37 (the line between the camera and the collision makes an angle 37° with respect to the north)

According to the law of momentum conservation:

For the x - component

m₁u₁ = (m₁ + m₂) Vsinθ

m₁u₁ = (m₁ + m₂) Vsin37

(795*35) = (795 + 3360) * Vsin37

27825 = 2500.54V

V = 27825/2500.54

V = 11.13 m/s

For the y - component

m₂u₂ = (m₁ + m₂) Vcos37

3360*u₂ = (795+3360) * 11.13*cos37

3360*u₂ = 36933.02

u₂ = 36933.02/3360

u₂ = 11 m/s