question_answer

A pebble is thrown horizontally from the top of a 20 m high tower with an initial velocity of 10 m/s. The air drag is negligible. The speed of the pebble when it is at the same distance from top as well as base of the tower \[(g=10\,m/{{s}^{2}})\]

A) \[10\sqrt{2}\,\,m/s\]                   

B) \[10\sqrt{3}\,\,m/s\]

C) 20 m/s              

D) 25 m/s

Correct Answer: B

Solution :

The pebble is at same distance from top and base of the tower after it falls down by a distance \[h=10\,m.\]

Applying conservation of energy.

\[\frac{1}{2}m{{v}^{2}}=\frac{1}{2}m{{u}^{2}}+mgh\]

or         \[{{v}^{2}}={{u}^{2}}+2gh=100+2\times 10\times 10=300\]

\[\therefore \]      \[v=10\sqrt{3}\,m/s.\]