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Q.

A projectile is fired with a velocity u at right angle to a slope, which is inclined at an angle $θ$ with the horizontal. The range of the projectile on the incline is

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a

$\frac{2 u^{2} \sin θ}{g}$

b

$\frac{2 u^{2}}{g} \tan θ \sec θ$

c

$\frac{u^{2}}{g} \sin 2 θ$

d

$\frac{2 u^{2}}{g} \tan θ$

answer is B.

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Detailed Solution

Let projectile strikes the plane at B, and its time of flight is T,
$y = u_{y} t + \frac{1}{2} a_{y} t^{2} 0 = u T - \frac{g \cos θ T^{2}}{2} T = \frac{2 u}{g \cos θ} R = A B = u_{x} T + \frac{1}{2} a_{x} T^{2} R = \frac{1}{2} a_{x} T^{2} R = \frac{1}{2} g \sin θ \frac{4 u^{2}}{g^{2} \cos^{2} θ} R = \frac{2 u^{2}}{g} \tan θ \sec θ$
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A projectile is fired with a velocity u at right angle to a slope, which is inclined at an angle θ with the horizontal. The range of the projectile on the incline is