Question

A body is projected horizontally with a speed $V_0$. Find the velocity of the body when It covers equal distances in horizontal and vertical directions.

• A. $v=2v_0$
• B. $v=\sqrt{5}{v}_0$
• C. $v=v_0/2$
• D. $v=\sqrt{3}{v}_0$

Answer 1

The correct option is B $v=\sqrt{5}{v}_0$

Lets consider, $v_x=v_0=$ horizontal speed,

The horizontal distance covered by a body in time $t$ is

$R=v_{0}t$

The vertical distance covered in time $t$ is

$H=\frac{1}{2}g{t}^2$

According to question,

$H=R$

$\frac{1}{2}g{t}^2=v_{0}t$

$t=\frac{2v_0}{g}$

Vertical velocity of a body,

$v_y=gt=g\times \frac{2v_0}{g}$

$v_y=2v_0$

The resultant velocity, $v=\sqrt{v_x^2+v_y^2}$

$v=\sqrt{v_0^2+4v_0^2}$

$v=\sqrt{5}{v}_0$

The correct option is B.