An elite aerials skier will leave a \'triple kicker\' (the biggest of the ramps)

Question

An elite aerials skier will leave a 'triple kicker' (the biggest of the ramps) with a velocity of 22 m/s. The ramp is angled quite steeply (70 degrees with respect to the horizontal) and the height of the ramp is 8 m above the surface of the water on which they will land. Using this information, compute and/or provide input on the following:

a. The vertical and horizontal velocities of the skier at takeoff

b. The height the athlete will attain above the water surface

c. The vertical and horizontal velocities of the skier when he/she hits the pool

d. Discuss the ramifications of landing in a pool and how this training experience night differ from what they athlete would experience in on-snow training or competition.

Explanation / Answer

here,

velocity, v = 22 m/s
Theta, A = 70 degrees
height of ramp, h = 8m

Part A:
horizontal velocity, vx = 22 * cos70 = 7.52 m/s
vertical velocity, vy = 22 * Sin70 = 20.67 m/s

Part B:
height attained by skier , H = ( v^2 * Sin^2(A) ) / 2g
H = (22^2*Sin^2(70))/(2*9.8)
H = 21.8 m

Total Height from water surface = 21.8 + 8 = 29.8 m

Part C:
Horizontal velocity will remain same as initial one Vx.

vertical Velocity, vy
vy = sqrt(2*g*h)
vy = sqrt(2*9.8*29.8)
vy = 24.167 m/s

Part C:
the ramp are longer (slope) and higher for snow competetion to compensate low friction between boards and snow. This will result in tilting of athelete towards front to help him better landing.

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