When a body is shot from the bottom of a long smooth inclined plane kept at an angle 30° with horizontal, it can travel a distance x along the plane. But when the inclination is increased to 60° and the same body is shot with the same velocity, it can travel y distance then x: y will be

Question

When a body is shot from the bottom of a long smooth inclined plane kept at an angle 30° with horizontal, it can travel a distance x along the plane. But when the inclination is increased to 60° and the same body is shot with the same velocity, it can travel y distance then x: y will be (A) √3: 1 (B) 1: √3 (C) 2: √3 (D) 1: √2

Tardigrade Admin · Accepted Answer

(x/y)=(u2/2 g sin 30°)=( sin 60°/ sin 30°) =((√3/2)/(1)2)=(√3/2) × (2/1)=√3 (u2/2 g sin 60°)

$3 : 1$

$1 : 3$

$2 : 3$

$1 : 2$

$\frac{x}{y} = \frac{u ^{2}}{2 g s i n 3 0 ^{\circ}} = \frac{s i n 6 0 ^{\circ}}{s i n 3 0 ^{\circ}}$
$= \frac{\frac{3}{2}}{\frac{1}{2}} = \frac{3}{2} \times \frac{2}{1} = 3$
$\frac{u ^{2}}{2 g s i n 6 0 ^{\circ}}$

Q. When a body is shot from the bottom of a long smooth inclined plane kept at an angle 30∘ with horizontal, it can travel a distance x along the plane. But when the inclination is increased to 60∘ and the same body is shot with the same velocity, it can travel y distance then x:y will be

3​:1

1:3​

2:3​

1:2​

yx​=2gsin30∘u2​=sin30∘sin60∘​ =21​23​​​=23​​×12​=3​ 2gsin60∘u2​

$3 : 1$

$1 : 3$

$2 : 3$

$1 : 2$

$\frac{x}{y} = \frac{u ^{2}}{2 g s i n 3 0 ^{\circ}} = \frac{s i n 6 0 ^{\circ}}{s i n 3 0 ^{\circ}}$
$= \frac{\frac{3}{2}}{\frac{1}{2}} = \frac{3}{2} \times \frac{2}{1} = 3$
$\frac{u ^{2}}{2 g s i n 6 0 ^{\circ}}$