Question

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

• A. $\sqrt{2 g h+u^{2}}: u$
• B. $1: 2$
• C. $1: 1$
• D. $\sqrt{2 g h+u^{2}}: \sqrt{2 g h}$

Answer 1

Answer: (C)

When particle is thrown in vertical downward direction with velocity $u$, then the final velocity at the ground level is
$v^{2} =u^{2}+2 g h $
$\therefore v =\sqrt{u^{2}+2 g h}$
Another particle is thrown horizontally with same velocity then at the surface of earth.

Horizontal component of velocity
$v_{x} = u$
Therefore, resultant velocity,
$v = \sqrt{u^2 + 2gh}$
For both the particles, final velocities when they reach the earth's surface are equal.