You are designing a ski jump ramp for the next Winter Olympics.You need to calcu

Question

You are designing a ski jump ramp for the next Winter Olympics.You need to calculate the vertical height ‘h’ from thestarting gate to the bottom of the ramp. The skiers push off hardwith their ski poles at the start, just above the starting gate, sothey typically have a speed of 3.7 m/s as they reach the gate. Forsafety, the skiers should have a speed of no more than 30.0 m/swhen they reach the bottom of the ramp. You determine that for a85.0 kg skier with good form, friction and air resistance will do atotal of –5,045 J of work on him during his run down theslope. What is the maximum height ‘h’ for which themaximum safe speed will not be exceeded?

Give your answer in meters to the first decimal place

Explanation / Answer

K1 = (1/2) m v12 m = 85 kg      (given) v1 = 3.7 m/s   (given)

U1 = m g h1 m = 85kg         (given) g = 9.8m/s2        (gravity) "h1" is our target variable.

Wother = -5,045J      (Friction and air resistancedo work on the skiers).

K2 = (1/2) m v22 m = 85 kg      (given) v2 = 30 m/s    (given)

U2 = m g h2 m = 85 kg      (given) g = 9.8 m/s2    (given) h2 = 0m         (the bottomof the slope is taken to be the zero position) This equation reduces to U2 = 0 J

Now, the equation looks like this:
m g h1 = (1/2) m v22 - (1/2)m v12 - Wother h1 = ( (1/2) m v22 -(1/2) m v12 - Wother ) / (m g)

solve for h1
h1 = ( (1/2) m v22 -(1/2) m v12 - Wother ) / (m g)

solve for h1

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