Two projectiles having different masses m1 and m2 are projected at an angle α and (90°-α) with the same speed from some point. The ratio of their maximum heights is

Question

Two projectiles having different masses m1 and m2 are projected at an angle α and (90°-α) with the same speed from some point. The ratio of their maximum heights is (A)  cot α: sin α (B) 1: 1 (C)  tan 2 α: 1 (D) 1: tan α

Tardigrade Admin · Accepted Answer

Maximum height, H=(u2 sin 2 α/2 g) For same speed of projection, H propto sin 2 α ∴ (H1/H2) =( sin 2 α/ sin 2(90°-α)) =( sin 2 α/ cos 2 α)= tan 2 α

Q. Two projectiles having different masses $m_{1}$ and $m_{2}$ are projected at an angle $α$ and $(9 0^{\circ} - α)$ with the same speed from some point. The ratio of their maximum heights is

$cot α : sin α$

$1 : 1$

$tan^{2} α : 1$

$1 : tan α$

Maximum height, $H = \frac{u ^{2} s i n ^{2} α}{2 g}$
For same speed of projection,
$H \propto sin^{2} α$
$∴ \frac{H _{1}}{H _{2}} = \frac{s i n ^{2} α}{s i n ^{2} ( 9 0 ^{\circ} - α )}$
$= \frac{s i n ^{2} α}{c o s ^{2} α} = tan^{2} α$

Q. Two projectiles having different masses m1​ and m2​ are projected at an angle α and (90∘−α) with the same speed from some point. The ratio of their maximum heights is

cotα:sinα

1:1

tan2α:1

1:tanα