A skier (m=57.0 kg) starts sliding down from the top of a ski jump with negligib

Question

A skier (m=57.0 kg) starts sliding down from the top of a ski jump with negligible friction and takes off horizontally.

(a) If h = 4.60 m and D = 10.2 m, find H.

[From h you can find the time of freefall, and thus find the skier's velocity as she takes off horizontally. Use conservation of energy. Neglect any effect from the air, which plays an important role in real ski-jumping]

(b) Find her total kinetic energy as she reaches the ground.

A skier (m=57.0 kg) starts sliding down from the top of a ski jump with negligible friction and takes off horizontally. If h = 4.60 m and D = 10.2 m, find H. [From h you can find the time of freefall, and thus find the skier's velocity as she takes off horizontally. Use conservation of energy. Neglect any effect from the air, which plays an important role in real ski-jumping] Find her total kinetic energy as she reaches the ground.

Explanation / Answer

let t is the time taken to fall h=4.6 m

h = 0.5*g*t^2


t = sqrt(2*h/g)

= 0.9689 s

v = D/t = 10.2/0.9689 = 10.53 m/s

0.5*m*v^2 = m*g*(H-h)

0.5*v^2 = g*(H-h)


H = 0.5*v^2/g + h

= 0.5*10.53^2/9.8 + 4.6

= 10.25 m

b)

KE = m*g*H = 57*9.8*10.25 = 5728 J

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