First slide

Projection Under uniform Acceleration

Question

A body is projected such that it has maximum range ‘R’ in the absence of wind. If wind imparts a horizontal acceleration of $\frac{g}{4}$ then the new range is

Moderate

A

$\frac{4 R}{3}$
B

R
C

$\frac{5 R}{4}$
D

$\frac{3 R}{2}$

Solution

as acceleration is in horizontal direction it will not change the time of flight and maximum height new range
$w i t h a c c e l e r a t i o n b e c o m e s R' = u \cos θ T + \frac{1}{2} (\frac{g}{4}) T R' = R + \frac{1}{2} (\frac{g}{4}) {(\frac{2 u \sin θ}{g})}^{2} R' = R + \frac{g}{8} \frac{4 u^{2} \sin^{2} θ}{g} = R + H b u t i f θ = 45^{0} H = \frac{R}{4} s o R' = R + \frac{R}{4} = \frac{5 R}{4}$

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