An pickup truck with mass 1.85 103 kg is traveling eastbound at +14.0 m/s, while

Question

An pickup truck with mass 1.85 103 kg is traveling eastbound at +14.0 m/s, while a compact car with mass 9.47 102 kg is traveling westbound at -14 m/s. (See figure.) The vehicles collide head-on, becoming entangled.Suppose the same two vehicles are both traveling eastward, the compact car leading the pickup truck. The driver of the compact car slams on the brakes suddenly, slowing the vehicle to 5.12 m/s. If the pickup truck traveling at 17.9 m/s crashes into the compact car, find the following.
a) the speed of the system right after the collision, assuming the two vehicles become entangled
b) the change in velocity for both vehicles
c) the change in kinetic energy of the system, from the instant before impact (when the compact car is traveling at 5.12 m/s) to the instant right after the collision

Explanation / Answer

(a)if you are seeking the solution for the second situation,
then, conserving momentum in horizontal direction and assuming the compact car is travelling with the same speed as the truck,we get

1850*17.9+947*5.12=(1850+947)*v

so v=13.51 m/s  <----answer (a)

(b)change in velocity of the truck=13.51-17.9=-4.39m/s

  change in velocity of the compact car=13.51-5.12=8.39m/s

 

(c) change in K.E=.5*(1850+947)*13.51^2-(.5*1850*17.9^2+.5*947*5.12^2) =53.5kJ

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