question_answer

A stone thrown vertically upwards from the top of a tower with an initial velocity u reaches the ground with a velocity 3u. Find the height of the tower.

Answer:

Velocity of the stone on reaching the foot of the tower is \[v=\sqrt{{{u}^{2}}+2gh}\Rightarrow 3u=\sqrt{{{u}^{2}}+2gh}\] \[\Rightarrow 9{{u}^{2}}={{u}^{2}}+2gh\Rightarrow h=\frac{4{{u}^{2}}}{g}\]