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Q.

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

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a

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

b

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

c

(R + 2H),H

d

(R + H),H

answer is D.

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Detailed Solution

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

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