Question

Two particles are projected from the same point with the same speed $u$ such that they have the same range $R$, but different maximum heights, $h_1$ and $h_2$. Which of the following is correct ?

• A. $R^2 \, = \, 2 h_1 h_2$
• B. $R^2 \, = \, 16 h_1 h_2$
• C. $R^2 \, = \, 4 h_1 h_2$
• D. $R^2 \, = \, h_1 h_2$

Answer 1

Answer: (B)

$R^2 \, = \, 16 h_1 h_2$

Answer 2

For same range angle of projection will be $\theta$ &
$90 - \theta$
$R = \frac{u^2 2 sin \theta cos \theta}{g}$
$h_1 = \frac{u^2 sin^2 \theta}{g}$
$h_2 = \frac{u^2 sin^2 (90 - \theta}{g}$
$\frac{R^2}{h_1h_2} = 16$