Question

A boy can throw a stone up to a maximum height of $10\text{m}$. The maximum horizontal distance that the boy can throw the same stone up to will be

• A. $20\sqrt{2}\text{m}$
• B. $10\text{m}$
• C. $10\sqrt{2}\text{m}$
• D. $20\text{m}$

Answer 1

The correct option is D $20\text{m}$

Let $u$ be the projected velocity of stone. So,

$R=\frac{u^2\sin 2\theta }{g}\&H=\frac{u^2{\sin }^2\theta }{2g}$

$H_{max}$ will be at $\theta ={90}^{\circ }$,

$H_{max}=\frac{u^2}{2g}$

$\Rightarrow u^2=20g(\because H_{max}=10\text{m})$

Now,
$R=\frac{u^2\sin 2\theta }{g}\Rightarrow R_{max}=\frac{u^2}{g}$

$R_{max}=\frac{20g}{g}=20\text{metre}$

Therefore, option $\left(\text{D}\right)$ will be the correct answer.