Physics Velocity Question

Question

A 1,500 kg car travelling at a velocity of 10m/s hits into a 2,250 kg truck that is at rest. If all of the car's momentum is lost to the truck, meaning that it is at rest after the collision, what is the truck's velocity after the collision? (Assume elastic, head-on collision and that momentum is conserved).

Answer 1

It's been a while since I've done this problem. But, I believe this is the way you do it: use the following equation:

m₁v_1i + m₂v_2i = m₁v_1f + m₂v_2f m₁ = 1,500 kg, v_1i = 10 m/s and m₂ = 2,250 kg, v_2i = 0 m/s

The trick is that v_1f = v_2f and this is because the two masses are 'stuck' together and move as one body.

Thus, doing some algebra you get the final eqn: ( m₁v_1i + m₂v_2i)/(m₁ + m₂) = v_f

Now, plug and chug you should get a logical answer.

Answer 2

m = mass of car

v = initial speed of car (final speed is zero)

M = mass of truck

u = final speed of truck (initial speed is zero)

Conservation of momentum:

mv + M(0) = m(0) + Mu

mv = Mu

u = (m/M)v

You know m, M, and v. Now plug in the numbers and get u in m/s.