First slide

Projection Under uniform Acceleration

Question

If R is the range of a projectile on a horizontal plane and h its maximum height, the maximum horizontal range with the same velocity of Projection is:

Moderate

A

2h
B

R² /8h
C

$2 R + \frac{h^{2}}{8 R}$
D

$2 h + \frac{R^{2}}{8 R}$

Solution

$R = \frac{2 u^{2} sinθcosθ}{2 g} and h = \frac{u^{2} \sin^{2} θ}{2 g}$
$\Rightarrow R^{2} = \frac{4 u^{4} {sinθ}^{2} {cosθ}^{2}}{g^{2}}$
$\frac{R^{2}}{8 h} = \frac{u^{2}}{g} - 2 h \Rightarrow maximum range = \frac{u^{2}}{g} = \frac{R^{2}}{8 h} + 2 h$

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