Question

A man can throw a stone to a maximum distance of $80m$. The maximum height to which it will rise in meter is:

• A. $30m$
• B. $20m$
• C. $10m$
• D. $40m$

Answer 1

Answer: (B)

$20m$

Let the speed by which the stone is thrown be $u$ making an angle $\theta$ with the horizontal.

$\therefore$ Horizontal range $R=\frac{u^{2}sin2\theta }{g}$

For maximum horizontal range $\theta ={45}^o$

$⟹$ $R_{max}=\frac{u^{2}sin{90}^o}{g}=\frac{u^2}{g}$

$80=\frac{u^2}{10}$ $⟹u^2=800$

Let maximum height it attains be $H$

$\therefore$ $H=\frac{u^{2}si{n}^2\theta }{2g}$ where $\theta ={45}^o$

$H=\frac{u^{2}si{n}^2{45}^o}{2g}=\frac{800\times \frac{1}{2}}{2\times 10}=20$ $m$