Question

Figure shows a ski-jump. A skier of mass 60 kg stands at P at the top of the ski-jump. He moves from P to Q and takes off for his jump at Q.

1. Calculate the change in the gravitational potential energy of the skier between P and Q.
2. If 75% of the energy in part (a) becomes the kinetic energy at Q, calculate the speed at which the skier arrives at Q.

Answer 1

Given:

Mass of skier, m = 60kg

Let the vertical drop from P to Q be hh m.

g = 10 m s⁻²

(a) Change in gravitational potential energy:

Δ PE = mgh

= 60 × 10 × h

= 600 h J

(b) Since 75 % of this energy becomes kinetic energy at Q:

K.E. = 75% of 600 h

= `75/100 xx 600  h`

= 450 h

Now,

450 h = `1/2 mv^2`

450 h = `1/2 xx 60 xx v^2`

450 h = 30 × v²

`v^2 = 450/30`

v² = 15 h

`v^2 = sqrt(15 h)  m  s ^-1`

So, once the height difference hh between P and Q is taken from the figure, the numerical answers can be found directly.