Question

A man standing on the roof of a house of height throws one particle vertically downwards and another particle horizontally with the same velocity . The ratio of their velocities when they reach the earth's surface will be

• A. : u
• B. 1 : 2
• C. 1: 1
• D.

Answer 1

The correct option is C 1: 1

When particle thrown in vertical downward direction with velocity u then final velocity at the ground level


v = $\sqrt{u^2+2gh}$
$v^2=u^2+2gh\therefore v=\sqrt{u^2+2gh}$

Another particle is thrown horizontally with same velocity then at the surface of earth.


$v_x=u$

$v_y=\sqrt{2gh}$
Horizontal component of velocity $v_x$=u

$\therefore$ Resultant velocity, v = $\sqrt{u^2+2gh}$

For both the particle final velocities when they reach the earth's surface are equal.