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

Solution

$H^{'} = H$ (as vertical component of acceleration has not changed)
$R = u_{x} T + \frac{1}{2} a_{x} T^{2} = R + \frac{1}{2} \times \frac{g}{4} \times \frac{4 u^{2} \sin^{2} θ}{g^{2}}$
$= R + \frac{u^{2} \sin^{2} θ}{2 g} = (R + H)$

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