A man cycles up a bill whose slope is 1 in 20 with a velocity of 6.4 km h^–1 along the hill. The weight of the man and the cycle is 98 kg. What work per minute is the man doing? What is his horse power? 

The slope of incline is 1 in 20.

This means sinθ = 1/20

where θ is the angle of inclination with the horizontal, figure.

v = 6.4 km h⁻¹ = (6.4 × 1000)/(60 × 60)ms⁻¹

=6400 ms⁻¹/3.600 =16/9ms⁻¹

m = 98kg

t = 1min = 60s

W = ? H.P. = ?

As is clear from figure force applied in moving up the incline is

F = mg sinθ

As Power = force × velocity

∴   P = mg sinθ × v

P = (98 × 9.8) ×1/20×16/9 watt

As 1 horse power = 746 watt

∴   Horse power of the person

=(98 × 9.8)/20 ×16/(9 × 746) = 0.114

As work done = power × time

∴   W =(98 × 9.8 × 16)/(20 × 9)× 60 = 5122.1J