Question

A man cycles up a hill rising 1 metre vertically
for every 50 metres along the slope. Find the
power of the man, if he cycles up at the rate of
3.6 km/hr. The weight of the cycle and man is
equal to 120kg. Neglect force of friction.
(1) 32.25 watt (2) 23.52 watt
(3) 25.32 watt (4) 52.32 watt​

Answer 1

Given :

• man cycles up a hill rising 1 meter vertically for every 50 meters along the slope .
• speed of cycle , v = 3.6 km/hr = 1 m/s .
• weight of the cycle and man , w = 120 kg .

To find :

Power of the man .

Solution :

We know , power is given by :

$P=F.v\\\\P=Fv$           ....... ( 1 )

( Here , $\theta=0^o$ . therefore $cos\ \theta = 1$ )

Here , F is the component of force along the slope .

Therefore ,

$F=mgsin\ \theta\\\\F=120\times 10\times \dfrac{1}{50}\\\\F=24 \ N$

Putting value of F in equation 1 .

We get :

$P=24\times 1\\P=24 \ Watt$

Power of the man is 24 watt .

Hence , this is the required solution .