Question

A body of mass $m$ is projected horizontally with a velocity $v$ from the top of a tower of height $h$ and it reaches the ground at a distance $x$ from the foot of the tower. If a second body of mass $2m$ is projected horizontally from the top of a tower of height $2h$, it reaches the ground at a distance $2x$ from the foot of the tower. The horizontal velocity of the second body is

• A. $v$
• B. $2v$
• C. $\sqrt{2}v$
• D. $\frac{v}{2}$

Answer 1

The correct option is C $\sqrt{2}v$

The horizontal distance travelled by a body pojected from height $h$ with horiziontal velocity $u$ is
$x=u\sqrt{\frac{2h}{g}}$
which is independent of the mass.

$\frac{u_1}{u_2}=\frac{x_1}{x_2}\times \sqrt{\frac{h_2}{h_1}}=\frac{x}{2x}\times \sqrt{\frac{2h}{h}}=\frac{1}{\sqrt{2}}$

Therefore, velocity of second body
$u_2=u_1\sqrt{2}=\sqrt{2}v$