A rocket is moving up with a velocity u.
Question:

A rocket is moving up with a velocity $u$. If the velocity of this rocket is suddenly tripled, what will be the ratio of two kinetic energies?

Solution:

$\mathrm{K}_{1}=\frac{1}{2} m v^{2}$

$\mathrm{K}_{2}=\frac{1}{2} m(3 v)^{2}=\frac{9}{2} m v^{2}$

$\therefore \frac{\mathrm{K}_{1}}{\mathrm{~K}_{2}}=\frac{1}{9}$ or $\mathrm{K}_{2}=9 \mathrm{~K}_{1}$