Question

An object is thrown at an angle of ${45}^{\circ }$ with the horizontal direction. The horizontal range of the particle is equal to _____

• A. Vertical Height
• B. Twice the vertical height
• C. Thrice the vertical height
• D. Four times the vertical height

Answer 1

The correct option is D

Four times the vertical height

We know R = $\frac{u^{2}sin2\theta }{g}$ = $\frac{u^{2}sin{90}^{\circ }}{g}$
$R=\frac{u^2}{g}$- - - - - (1),
As $\theta$=${45}^{\circ }$
$H=\frac{u^{2}si{n}^2\theta }{2g}$ = $\frac{u^{2}si{n}^2{45}^{\circ }}{2g}$ = $\frac{u^2}{4g}$ - - - - (2)
From (1) & (2)
R = 4H