Question

In aerial skiing, skiers use gravity to accelerate down a slope, called a in-run, before going onto a take-off ramp and jumping and performing aerial tricks. A 60 kg skier competes in a competition where the in-run is 70 m long and is angled at 25? below the horizontal, and the take-off ramp is 3 m high. Ignore friction and drag.

(a) How much work has gravity done on the skier when they reach the end of the in-run?

(b) What is the speed of the skier at the end of the in-run?

(c) What is the speed of the skier as they leave the take-off ramp?

(d) Would you expect the maximum height the skier reaches after leaving the take-off ramp to be higher than, equal to, or lower than their height at the beginning of the in-run? Explain your answer.

Answer 1

a)

Work done by gravity on the skier when he reaches the end of the in-run is

b)

Height of in-run ramp is

Initially when the Skier starts from a height on the top of in-run ramp , he has only potential energy,

when he reaches the end of in-run he has only kinetic energy

Conserving the enegy of skier at the two positions,

Speed of skier at the end of in-run is

c)

Starting with this initial velocity the Skiier reaches the top of take-off ramp with velocity  

Height of take-off ramp is

Energy of skiier at the top of the take-off ramp is

conserving energy at the starting point from in-run and leaving point of take-off ramp ,

The speed of the skier as they leave the take-off ramp is

d)

Let the take-off be inclined at an angle with the horizontal. The trajectory of Skiier will be that of a projectile with horizontal velocity and vertical velocity . At the maximum height of the parabolic trajectory of projectile , vertical velocity will be zero. But horizontal velocity will be the same as initial horizontal velocity .

Conserving energy at initial height and maximum height reached after leging take-off ramp ,

means  

That is the maximum height the skier reaches after leaving the take-off ramp is less than the height at the beginning of the in-run.