Question

A man is riding on a cycle with velocity $7.2km/hr$ up a hill having a slope $1$ in $20$. The total mass of the man and cycle is $100kg$. Take $g=9.8m/s^2$. The power of the man is-

• A. $98W$
• B. $49W$
• C. $196W$
• D. $147W$

Answer 1

The correct option is A $98W$

$\text{Step 1: Understanding the Slope}$ $\text{[Refer Fig.]}$

An incline having a slope 1 in 20 means that height of incline increases by 1 unit on going 20 units distance along the incline.

So, In $\Delta ABC:$

$\sin \theta =\frac{BC}{AB}=\frac{1}{20}$

$\text{Step 2: Newton's Second law}$

Since the velocity is constant, therefore acceleration will be zero

$\Rightarrow F_{Net}=0$

$\Rightarrow F-mg\sin \theta =0$

$\Rightarrow$ $F=mg\sin \theta$

$\text{Step 3: Power Calculation}$

Given, Velocity $v=7.2km/hr=7.2\times \frac{5}{18}m/s=2m/s$

Power is given by

$P=$ $\overrightarrow{F}.\overrightarrow{v}=Fvcos{0}^o=mg\sin \theta v$

Putting given values:

$\Rightarrow P=100\left(kg\right)\times 9.8\left(m/s^2\right)\times \frac{1}{20}\times 2m/s$

$\therefore P=98$ Watt

Hence $A$ is the correct option.