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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 to B 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 skier arrives at B.
$$(Take \,g=10\, m\, s^{-1})$$

Solution
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(a) Mass of skier $$= 60\,kg$$
Loss in potential energy $$= mg(h_1 -h_2)$$
$$ 60 \times 10 \times (75 -15) $$
$$= 60 \times 10 \times 60 = 3.6 \times 10^4\, J$$
(b) Kinetic energy at $$B = \dfrac{75}{100} \times 3.6 \times 70^4 = 27000 \, J$$
$$ = 2.7 \times 10^4\, J$$
Kinetic energy $$=\dfrac{1}{2} mv^2$$
$$27000 =\dfrac {1}{2} mv^2$$
$$27000 =\dfrac {1}{2} \times 60 \times v^2$$
$$v^2 =\dfrac {27000}{30} = 900$$
$$V= 30/, m/s$$

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