Question

The diagram given below shows a ski jump. A skier weighing 60 kgf stands at A at the top of ski jump. He moves from A and takes off for his jump at B.
a: calculate the change in the gravitational potential energy of the skier between A and B.
b: If 75% of the energy in part (a) becomes kinetic energy at B, calculate the speed at which the arrives at B.​​

Answer 1

Given that,

Weight = 60 kgf

Height of A= 75 m

Height of B= 15 m

We need to calculate the change in the gravitational potential energy of the skier between A and B

Using formula of potential energy

$\text{loss of potential energy}=mg(h_{1}-h_{2})$

Where, m = mass

g = acceleration due to gravity

$h_{1}$ = height of A

$h_{2}$ = height of B

Put the value into the formula

$\text{loss of potential energy}=60\times9.8\times(75-15)$

$\text{loss of potential energy}=3.5\times10^{4}\ J$

(b). If 75% of the energy in part (a) becomes kinetic energy at B,

We need to calculate the kinetic energy at B

Using formula for kinetic energy

$K.E=\dfrac{75}{100}\times\text{loss of potential energy}$

$K.E=\dfrac{75}{100}\times3.5\times10^{4}$

$K.E=26250\ J$

We need to calculate the speed at which the arrive at B

Using formula of kinetic energy

$K.E=\dfrac{1}{2}mv^2$

Put the value into the formula

$26250=\dfrac{1}{2}\times60\times v^2$

$v^2=\dfrac{26250\times2}{60}$

$v=\sqrt{\dfrac{26250\times2}{60}}$

$v=29.58\ m/s$

Hence, (a). The change in the gravitational potential energy of the skier between A and B is $3.5\times10^{4}\ J$

(b). The speed at which the arrive at B is 29.58 m/s.