First slide

Projection Under uniform Acceleration

Question

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

Moderate

A

$u^{2} / g$
B

$2 u^{2} / g$
C

$u^{2} / 2 g$
D

$u^{2} / 4 g$

Solution

$y_{1} = \frac{(usin θ)^{2}}{2 g} and y_{2} = \frac{{\{usin (90^{\circ} - θ)\}}^{2}}{2 g}$
or $y_{2} = \frac{(ucos θ)^{2}}{2 g}$
$∴ y_{1} + y_{2} = \frac{u^{2}}{2 g} [\sin^{2} θ + \cos^{2} θ] = \frac{u^{2}}{2 g}$

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