First slide

Projectile motion

Question

The horizontal range and maximum height attained by a projectile are R and H, respectively. If a constant horizontal acceleration a = g/4 is imparted to the projectile due to wind then its horizontal range and maximum height will be

Moderate

A

$(R + H), \frac{H}{2}$
B

$(R + \frac{H}{2}), 2 H$
C

$(R + 2 H), H$
D

$(R + H), H$

Solution

$H = \frac{u^{2} \sin^{2} θ}{2 g}, R = \frac{u^{2} \sin 2 θ}{g}$
Maximum height will be same because acceleration a= g/4 is in horizontal direction
$R^{'} = ucos θT + \frac{1}{2} {aT}^{2} = R + \frac{1}{2} \frac{g}{4} {(\frac{2 usin θ}{g})}^{2} = R + H$

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