Question

You are designing a ski jump ramp for the next Winter Olympics. Youneed to calculate the vertical height^ h from the starting gate to the bottom of the ramp. Theskiers push off hard with their ski poles at the start, just abovethe starting gate, so they typically have a speed of 2.0^m/s as they reach the gate. For safety, the skiersshould have a speed of no more than 30.0^m/s when they reach the bottom of the ramp. Youdetermine that for a 86.0^ kg skier with good form, friction and air resistance will dototal work of magnitude 4000^ J on him during his run down the slope.What is themaximum height ^h for which the maximum safe speed will not be exceeded?

Answer 1

Answer:

$H = 50.5 m$

Explanation:

As we know by work energy theorem that work done by all forces is equal to change in kinetic energy

So we know that

$W_f + W_g = \frac{1]{2}mv_f^2 - \frac{1}{2}mv_i^2$

so we know that

$W_f = -4000 J$

$v_f = 30 m/s$

$v_i = 2 m/s$

$m = 86 kg$

now we have

$mgH - 4000 = \frac{1}{2}(86)(30^2 - 2^2)$

$86(9.81)(H) - 4000 = 43(900 - 4)$

$H = 50.5 m$