Question

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

Answer 1

Dear Student,

$$\begin{gathered} \mathrm{Let}\mathrm{h}\mathrm{be}\mathrm{the}\mathrm{height}\mathrm{of}\mathrm{the}\mathrm{tower}. \\ \Rightarrow {\mathrm{v}}^2={\mathrm{u}}^2+2\mathrm{aS} \\ \Rightarrow {\left(-3\mathrm{u}\right)}^2={\mathrm{u}}^2+2\left(-\mathrm{g}\right)\left(-\mathrm{h}\right) \\ \Rightarrow 9{\mathrm{u}}^2={\mathrm{u}}^2+2\mathrm{gh} \\ \Rightarrow 8{\mathrm{u}}^2=2\mathrm{gh} \\ \Rightarrow \mathrm{h}=\frac{8{\mathrm{u}}^2}{2\mathrm{g}} \\ \Rightarrow \mathrm{h}=\frac{4{\mathrm{u}}^2}{\mathrm{g}} \end{gathered}$$