Question

A freestyle skier is training for the Olympics. In this sport the skier starts at the top of the hill and skis straight towards a ramp. She then skis up the ramp and launches herself into the air. The skier and skis have a total mass of 70 kg. The coefficient between the skis and the snow is .05. The downhill slope is at a 40 degree angle to the horizontal.

a) Draw the free body diagram of the skier going down the hill(include all the forces acting on the skier)

b) The distance from the start of the run to the start of the uphill ramp is 40 m. What is the velocity of the skier as she enters the ramp?

c) The ramp is directed upwards from the slope at an angle of 70 degrees. Draw the free body diagram of the skier going up the ramp(the angle of the ramp should be from the horizontal)

d) The ramp is 10 m long. It has the same coefficient of dynamic friction as the slope. What is the skier's resultant velocity as she leaves the ramp?

e) What is the vertical height at the end of the ramp from the horizontal?

f) What is the skier's horizontal and vertical velocity as she leaves the ramp?

g) How high does the skier get off the ground during the jump?

h) Since she lands in water, the water level is the same level as the base of the ramp. How long is she in the air?

i) What is her horizontal translation from the end of the ramp until she enters the water?

Answer 1

a)

b)
a = g*sin(40) - muek*g*cos(40)

= 9.8*sin(40) - 0.05*9.8*cos(40)

= 5.92 m/s^2

v^2 - u^2 = 2*a*s

here, u = 0

v = sqrt(2*a*s)

= sqrt(2*5.92*20)

= 15.4 m/s <<<<<<<<<<----------Answer

c)

d) a = -g*sin(70) - muek*g*cos(70)

= -9.8*sin(70) - 0.05*9.8*cos(70)

= -9.38 m/s^2

v^2 - u^2 = 2*a*s

here, 15.4 = 0

v = sqrt(u^2 + 2*a*s)

= sqrt(15.4^2 - 2*9.38*10)

= 7 m/s <<<<<<<<<<----------Answer

e) h = 10*sin(70)

= 9.4 m <<<<<<<<<----------Answer

f) vx = v*cos(70) = 7*cos(70) = 2.4 m/s <<<<<<<<<----------Answer

vy = v*sin(70) = 7*sin(70) = 6.58 m/s <<<<<<<<<----------Answer

g) H = h + vy^2/2*g

= 9.4 + 6.58^2/(2*9.8)

= 11.6 m <<<<<<<<<----------Answer

h) T = vy/g + sqrt(2*H/g)

= 6.58/9.8 + sqrt(2*11.6/9.8)

= 2.21 s <<<<<<<<<----------Answer

i) x = vx*T

= 2.4*2.21

= 5.3 m <<<<<<<<<----------Answer