If t_1 and t_2 are the times of flight of two particles having the same initial velocity u…

Question

If $t_1$ and $t_2$ are the times of flight of two particles having the same initial velocity $u$ and range $R$ on the horizontal, then $t_1^2+t_2^2$ is equal to:

Accepted Answer

For the same range, the projection angles are $\alpha$ and $\dfrac\pi2-\alpha$: $t_1=\dfrac{2u\sin\alpha}g$, $t_2=\dfrac{2u\cos\alpha}g$

$$t_1^2+t_2^2 = \frac{4u^2}{g^2}(\sin^2\alpha+\cos^2\alpha)=\frac{4u^2}{g^2}$$

Solutions · 1