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{\rm{ m/s}} as they reach the gate. For safety, the skiersshould have a speed of no more than 30.0 {\rm{ 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 {\rm 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=50.46m

Step-by-step explanation:

Our values are,

`m = 86kg`

`v_i = 2m/s`

`v_f = 30m/s`

`W= 4000J`

We only need to use conservative of energy,

`K_1 + U_1 = K_2 + U_2 + W`

`(1)/(2)mv_i^2 + mgh = (1)/(2)mv_f^2 +0 +4000`

`(1)/(2)(86)(2)^2+(86)(9.8)h = (1)/(2)(86)(30)^2 +4000`

`h=50.46m`