A gun fires two bullets at 60° and 30° with horizontal. The bullets strike at some horizontal distance. The ratio of maximum height for the two bullets is in the ratio of

Question

A gun fires two bullets at 60° and 30° with horizontal. The bullets strike at some horizontal distance. The ratio of maximum height for the two bullets is in the ratio of (A) 2: 1 (B) 3: 1 (C) 4: 1 (D) 1: 1

Tardigrade Admin · Accepted Answer

The bullets are fired at the same initial speed (H/H')=(u2 sin 2 60°/2 g) × (2 g/u2 sin 2 30°)=( sin 2 60°/ sin 2 30°) =((√3 / 2)2/(1 / 2)2)=(3/1)

Q. A gun fires two bullets at $6 0^{\circ}$ and $3 0^{\circ}$ with horizontal. The bullets strike at some horizontal distance. The ratio of maximum height for the two bullets is in the ratio of

$2 : 1$

$3 : 1$

$4 : 1$

$1 : 1$

The bullets are fired at the same initial speed
$\frac{H}{H ^{'}} = \frac{u ^{2} s i n ^{2} 6 0 ^{\circ}}{2 g} \times \frac{2 g}{u ^{2} s i n ^{2} 3 0 ^{\circ}} = \frac{s i n ^{2} 6 0 ^{\circ}}{s i n ^{2} 3 0 ^{\circ}}$
$= \frac{( 3 /2 ) ^{2}}{( 1/2 ) ^{2}} = \frac{3}{1}$

Q. A gun fires two bullets at 60∘ and 30∘ with horizontal. The bullets strike at some horizontal distance. The ratio of maximum height for the two bullets is in the ratio of

2:1

3:1

4:1

1:1