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 :

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TestHub · Accepted Answer

Let stone is projected with initial velocity $v$ .

Kinetic energy of the stone at point of projection is $K E_{1} = \frac{1}{2} m v^{2}$ .

Now, velocity of stone at maximum height is $= v \cos 30 °$ , so kinetic energy at that point is $K E_{2} = \frac{1}{2} m {(v \cos 30 °)}^{2}$

Hence, the ratio $\frac{K E_{1}}{K E_{2}} = \frac{\frac{1}{2} m v^{2}}{\frac{1}{2} m {(v \cos 30 °)}^{2}} = \frac{4}{3}$

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