Question

You are designing a ski jump ramp for the next Winter Olympics. You need to calculate the vertical height (h) from the starting gate to the bottom of the ramp. The skiers push off hard with their ski poles at the start, just above the starting gate, so they typically have a speed of 2.0 m/s as they reach the gate. For safety, the skiers should have a speed of no more than 30.0 m/s when they reach the bottom of the ramp. You determine that for a 85.0 kg skier with good form, friction and air resistance will do total work of magnitude 4000 J on him during his run down the slope.What is the maximum height (h) for which the maximum safe speed will not be exceeded?

Answer 1

h = 50.49 m

Step-by-step explanation:

Data provided:

Speed of skier, u = 2.0 m/s

Maximum safe speed of the skier, v = 30.0 m/s

Mass of the skier, m = 85.0

Total work = 4000 J

Height from the starting gate = h

Now, from the law of conservation of energy

Total energy at the gate = total energy at the time maximum speed is reached

`(1)/(2)mu^2+mgh=4000J+(1)/(2)mv^2`

where, g is the acceleration due to the gravity

on substituting the values, we get

`(1)/(2)*85*2.0^2+85*9.81* h=4000J+(1)/(2)*85*30^2`

or

170 + 833.85 × h = 4000 + 38250

or

h = 50.49 m