Question

A skier is pushed from the top of a hill so that he starts moving down the hillside from a height of 100 m with

an initial speed of 0.434 m/s. After traveling 80.4 m, he reaches the bottom of the valley. Due to inertia, he
then continues 70.4 m up another hillside (y = 40 m) and crashes into a snow bank that compressess like a
spring (k = 50 N/m). What is the skiers speed as he crashes into the snow bank? How far does the snow
compress? Assume that you can neglect friction.

Answer 1

Speed as the skier crashes into the snow bank: 0.434 m/s

Distance the snow compresses: 1.544 m

The speed of the skier as he crashes into the snow bank is the initial speed since there is no acceleration due to the lack of friction. The distance the snow compresses is calculated using the following equation:

compression = (mass x velocity2) / (2 x spring constant)

Therefore, compression = (75 kg x 0.4342) / (2 x 50 N/m) = 1.544 m