First slide

Projectile motion

Question

A ball is thrown at different angles with the same speed u and from the same point and it has the same range in both the cases. If y₁ and y₂ are the heights attained in the two cases, then y₁ + y₂ is equal to

Moderate

A

$\frac{u^{2}}{g}$
B

$\frac{2 u^{2}}{g}$
C

$\frac{u^{2}}{2 g}$
D

$\frac{u^{2}}{4 g}$

Solution

$\begin{array}{l} y_{1} = \frac{u^{2} \sin^{2} θ}{2 g}, y_{2} = \frac{u^{2} \sin^{2} (90^{\circ} - θ)}{2 g} = \frac{u^{2} \cos^{2} θ}{2 g} \\ \Rightarrow y_{1} + y_{2} = \frac{u^{2}}{2 g} \end{array}$

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