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 (in $meter$) is

Answer 1

Given,

$R_1=R_2$

Angle of projection$=\frac{\pi }{3}$

$H_{max}=102m$

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

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

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

${\theta }_1=\pi /3\Rightarrow {\theta }_2=\pi /2-\pi /3=\pi /6$

$H_2=\frac{H_1{\sin }^2{\theta }_2}{{\sin }^2{\theta }_1}=102\times \frac{1/4}{3/4}=34m$