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

`H = 50.5 m`

Step-by-step 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

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 = (1)/(2)(86)(30^2 - 2^2)`

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

`H = 50.5 m`