Two particles are projected from the same point with the same spe… - Vidyadip

MCQ

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
$R^2 = 4 h_1h_2$
B
$R^2 = 2 h_1h_2$
✓
$R^2 = 16 h_1h_2$
D
$R^2 = h_1h_2$

✓

Answer

Correct option: C.

$R^2 = 16 h_1h_2$

c
$\begin{array}{l} For\,same\,range\,angle\,of\,projection\,will\\ be\,\theta \,will\,be\,\theta \,\& \,90 - \theta \\ R\,\, = \,\frac{{{u^2}2\sin \theta \cos \theta }}{g}\\ {h_1} = \frac{{{u^2}{{\sin }^2}\theta }}{g}\\ {h_2} = \frac{{{u^2}\sin {\,^2}\left( {90 - \theta } \right)}}{g}\\ \frac{{{R^2}}}{{{h_1}{h_2}}} = 16 \end{array}$

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