The combined weight of a cyclist and his bicycle is 220 lb. What power must the cyclist produce to ride up a 5% grade at a constant speed of 10 mph?

The power developed by the man to ride the bicycle at constant speed is  0.2927 hp

Explanation:

Given the data in the question;

weight of cyclist and bicycle W = 220 lb

speed  v = 10 mph = 14.6667 ft/s

Angle of inclination θ = tan⁻¹( 5% ) = tan⁻¹( 0.05 ) = 2.86°

Now we calculate the power developed by the man,

Power = W( dh / dθ  )

Power = W( vsinθ )

we substitute

Power = 220 lb( 14.6667 ft/s × sin( 2.86 )

Power = 220 lb( 14.6667 ft/s × 0.04989569 )

Power = 160.997 ft.lb/s

Power = 160.997 ft.lb/s ( 1hp / 550 ft.lb/s )

Power = 0.2937 hp

Therefore, The power developed by the man to ride the bicycle at constant speed is 0.2927 hp

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