First slide

Projection Under uniform Acceleration

Question

A ball is thrown at different angles with the same speed $V_{o}$ from the same point on ground and it has same range in both cases. If the sum of maximum heights attained by the ball is 90m and $g = 10 m / s^{2}$ , find $V_{o}$

Moderate

Solution

If angle of projection in one case is α, angle of projection in the other case is $(90^{o} - α)$
$\begin{array}{l} ∴ H_{1} = \frac{{V_{0}}^{2} \sin^{2} α}{2 g} and H_{2} = \frac{{V_{0}}^{2} \sin^{2} (90^{o} - α)}{2 g} = \frac{{V_{0}}^{2} \cos^{2} α}{2 g} \\ ∴ H_{1} + H_{2} = \frac{{V_{0}}^{2}}{2 g} \Rightarrow V_{0} = \sqrt{2 g (H_{1} + H_{2})} = \sqrt{2 \times 10 \times 90} m / s = 30 \sqrt{2} m / s \end{array}$

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