An pickup truck with mass 1.79 10 3 kg is traveling eastbound at +14.1 m/s, whil

Question

An pickup truck with mass 1.79  103kg is traveling eastbound at +14.1 m/s, while a compact car with mass 8.78  102 kg is traveling westbound at -14.1 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 6.46 m/s. If the pickup truck traveling at 17.6 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
m/s

(b) the change in velocity for both vehicles

Please show work so I can learn how to do the problems

Explanation / Answer

a) conservation of momentum

1.79E3*14.1-8.78E2*14.1 = (1.79E3 + 8.78E2)*v

v=4.81979010495 m/s

b) dvtruck = 4.81979010495 -14.1=-9.28020989505

dvcar =4.81979 - (-14.1)= 18.91979

c)

dKE = KEfinal - KE initial

= 1/2*(1.79 E3+8.78E2)*4.819^2 - 0.5*1.79E3*14.1^2 - 0.5*8.78E2*14.1^2

=-56994.616826J


2) a) conservation of momentum

1.79E3*17.6 + 8.78E2*6.46 = (1.79E3 + 8.78 E2)*v
v= 13.933988006

b) dvtruck = 13.933988006 - 17.6 =-3.226011994

dvcar = 13.933988006 - 6.46=7.47398

c) dKE = Ke final - Ke intial

=1/2*(1.79E3+8.78E2)*13.9333^2 - 0.5*1.79E3*17.6^2 - 0.5*8.78E2*6.46^2

=-36587.968074 J

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