Question

Two stones are projected with the same speed but making different angles with the horizontal. Their ranges are equal. If the angle of projection of one is $\pi /3$ and its maximum height is $h_1$ then the maximum height of the other will be

• A. $3h_1$
• B. $2h_1$
• C. $h_1/2$
• D. $h_1/3$

Answer 1

The correct option is D $h_1/3$

Assuming the angle of projection is = π/3 radians:

$\frac{\pi }{2}-\frac{\pi }{3}=\frac{\pi }{6}radians$

$\Rightarrow$ the angle of projection of the other object

let the maximum heights be: $h_1$and $h_2$:

$\frac{h_1}{h_2}=\frac{si{n}^2\left(\frac{\pi }{3}\right)}{si{n}^2\left(\frac{\pi }{6}\right)}$

$\frac{h_1}{h_2}=\frac{{\left(\frac{\sqrt{3}}{2}\right)}^2}{{\left(\frac{1}{2}\right)}^2}$

$\frac{h_1}{h_2}=\frac{\left(\frac{3}{4}\right)}{\left(\frac{1}{4}\right)}=\frac{3}{1}$

$h_2=\frac{h_1}{3}$