A man of mass 60 kg falls from rest and slides down a ski-slope (without his ski

Question

A man of mass 60 kg falls from rest and slides down a ski-slope (without his skis) as shown (diagram not to scale). At point P, at which he has fallen a vertical height H meters as shown, his speed is vo =10 m/s. Assume he slides without any frictional force or air resistance acting on him until he reaches point P.

A11. The value of H is

A12. After point P, air resistance and friction cannot be ignored and have a significant effect on his subsequent motion. If 720 J of his mechanical energy at P are transformed into heat as he slides from P to Q, with what speed does he arrive at Q (note that this does NOT depend on your answer to A11)?

Explanation / Answer

change in height = 8 - 5 = 3 metres ;

gain in PE = mgh = 60 * 9.8 * 3 = 1764 J ;

L = loss in mechanical energy = - 720 J ;

K + P + L = 0 ;

or K = - ( P + L )

or K = - ( 1764 - 720 )

or K = - 1044 ;

or 0.5 m ( v2^2 - v1^2 ) = - 1044 J ;

or 0.5 * 60 ( v2^2 - 10^2 ) = -1044 ;

or v2 = 8.07465 m /s

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