Question

A body is projected vertically upward. If t1 and t2 are the times at which the body is at height h above the point of projection while ascending and descending respectively. Then h=?

Answer 1

Answer on question #59884, Physics - Mechanics - Relativity

Height h(t):

$$h(t) = v_0 * t - \frac{g t^2}{2}$$

Then,

$$\left\{ \begin{array}{l} h(t_1) = h = v_0 * t_1 - \frac{g t_1^2}{2} \\ h(t_2) = h = v_0 * t_2 - \frac{g t_2^2}{2} \end{array} \right.$$

From first, $v_0 = \frac{2h + g t_1^2}{2t_1}$,

From second, $v_0 = \frac{2h + g t_2^2}{2t_2}$.

In each equation, $v_0$ is the same, then

$$v_0 = \frac{2h + g t_1^2}{2t_1} = \frac{2h + g t_2^2}{2t_2}$$ $$2h \left(\frac{1}{t_1} - \frac{1}{t_2}\right) = g * (t_2 - t_1)$$ $$h = \frac{g * t_1 * t_2}{2}$$

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