First slide

Projection Under uniform Acceleration

Question

A stone is thrown at an angle $θ$ to the horizontal reaches a maximum height H. Then the time of flight of stone will be:

Moderate

A

$\sqrt{\frac{2 H}{g}}$
B

$2 \sqrt{\frac{2 H}{g}}$
C

$\frac{2 \sqrt{2 H \sin θ}}{g}$
D

$\frac{\sqrt{2 H \sin θ}}{g}$

Solution

H = $\frac{u^{2} \sin^{2} θ}{2 g} and T = \frac{2 u \sin θ}{g}$
or $T^{2} = \frac{4 u^{2} \sin^{2} θ}{g^{2}}$
$\frac{T^{2}}{H} = (\frac{4 u^{2} \sin^{2} θ}{g}) \times \frac{2 g}{u^{2} \sin^{2} θ} = \frac{8}{g}$
or $T^{2} = \frac{8 H}{g} \Rightarrow T = 2 \sqrt{\frac{2 H}{g}}$

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