Question

A skier is skiing down a hill on friction-less skies when he realizes there is a cliff in front of him. He skies right over the edge and lands on the valley floor. His motion has two parts: on the hill he started at rest and accelerated throughout his trip. Once he comes to the cliff edge, he goes over the side and is experiencing projectile motion through the air, until he lands. Assume the hill makes a 45 degree angle with the horizontal. Assume the cliff is about 10 meters above the valley floor. Ignore air resistance.

1. Make a free body diagram of the skier on the slope, including all forces labeled clearly.

2. You will have to estimate two values: the skier's mass, and either the distance or time during which he was accelerating down the slope. Estimate these values, providing explanations for your estimations.

3. What is his speed when he leaves the ski hill, according to your estimates?

4. What is the vertical component of the skier's velocity when he hits the valley floor?

5. During which section is the magnitude of the acceleration experienced by the skier the greatest? Justify your answer.

Answer 1

Q1.

free body diagram:

Q2.

let mass of the skier be 60 kg.

time for which he was acceleration is 5 seconds.

60 kg is an average weight of a normal, healthy human being.

5 seconds is a normal duration for driving down a slope.

Q3.

then velocity achieved at the end of 5 seconds

=initial velocity+accelertion along the direction of motion*time

=0+9.8*sin(45)*5

=34.648 m/s

Q4.

when he hits the valley floor, let vertical component of the cliff be v.

initial vertical speed=34.648*cos(45)=24.5 m/s

acceleration along vertical=9.8 m/s^2

distance to be covered=10 m

then v^2-24.5^2=2*9.8*10

==>v=sqrt(24.5^2+2*9.8*10)=28.218 m/s

Q5.

when he is falling from the cliff, acceleration is 9.8 m/s^2

when he is coming down hill, acceleration is 9.8*sin(pi/4)=6.9296 m/s^2

hence acceleration when he is falling from the cliff is higher.