Question

Two stones are projected with the same speed but making different angles with the horizontal. Their horizontal ranges are equal. The angle of projection of one is $\frac{\pi }{3}$ and the maximum height reached by it is $102m$. Then the maximum height reached by the other is:

• A. $336m$
• B. $224m$
• C. $56m$
• D. $34m$

Answer 1

Answer: (D)

$34m$

As horizontal ranges are equal:

$\frac{u^2\sin 2{\theta }_1}{g}=\frac{u^2\sin 2{\theta }_2}{g}$

$\Rightarrow \sin 2{\theta }_1=\sin 2{\theta }_2$

$\Rightarrow 2{\theta }_1=180-2{\theta }_2$

$\Rightarrow [{\theta }_1+{\theta }_2={90}^0]$

${\theta }_2={60}^0,{\theta }_1={30}^0$

$H_1=\frac{u^2{\sin }^2{\theta }_1}{2g}=?$

$H_2=\frac{u^2{\sin }^2{\theta }_2}{2g}=102$

$\frac{H_1}{H_2}=\frac{{\sin }^2{\theta }_1}{{\sin }^2{\theta }_2}$

$\frac{H_1}{H_2}=\frac{1}{3}\Rightarrow H_1=H_2/3=102/3=34m$