A stone is projected at angle $$30°$$ to the horizontal. The ratio of kinetic energy of the stone at point of projection to its kinetic energy at the highest point of flight will be:

Find the ratio of kinetic energy at the point of projection to the kinetic energy at the highest point for a stone projected at $$30°$$ to the horizontal.

The kinetic energy at the point of projection is $$KE_1 = \frac{1}{2}mv^2$$. At the highest point only the horizontal component of velocity remains, namely $$v_x = v\cos 30° = \frac{v\sqrt{3}}{2}$$, so the kinetic energy there is $$KE_2 = \frac{1}{2}mv_x^2 = \frac{1}{2}m \cdot \frac{3v^2}{4} = \frac{3}{4} \cdot \frac{1}{2}mv^2$$.

Therefore, the ratio of the kinetic energies is $$\frac{KE_1}{KE_2} = \frac{\frac{1}{2}mv^2}{\frac{3}{8}mv^2} = \frac{4}{3}$$, giving a ratio of $$4 : 3$$ which corresponds to Option D.