A car sits on the side of the road trying to sit out a blizzard. A passing truck

Question

A car sits on the side of the road trying to sit out a blizzard. A passing truck skids into the stationary car sending it sliding off the road. The car slides down a snowy hill, reaches a level valley floor, and continues to slide to a stop. Determine the height of the hill above the valley floor. Treat the positive direction as to the right. Solve symbolically if there had been enough info given to to determine the initial velocity of the car AFTER it was hit by the car. And if the angle is given

Explanation / Answer

There are multiple answers to this question. It really matters in what terms the answer should have.

Using the Principle of Conservation of Energy for the duration of time AFTER the collision, we can say:

PE + KE = PE + KE

Putting the beginning of the y-axis at the valley floor, we can say the final PE is 0.

mcgho + 1/2 mcv2 = 1/2 mcv2

gho + 1/2vo2 = 1/2vf2

1/2vo2 = 1/2vf2 - gho

vo2 = vf2 - 2gho

Answer: vo = (vf2 - 2gho)

OR

Using the Principle of Conservation of Linear Momentum:

mcvoc + mtvot = mcvf + mtvft

The car was trying to sit out the storm so we can assume it was stationary before the collision.

mtvot = mcvfc + mtvft

mcvfc =  mtvot -  mtvft

vfc =  (mtvot -  mtvft)/ mc

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