Average velocity of a particle in projectile motion between its starting point and the highest point of its trajectory is (projection speed = u, angle of projection from horizontal = $θ$ )

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$\frac{u}{2} \sqrt{1 + \cos^{2} θ}$

$\frac{u}{2} \sqrt{2 + \cos^{2} θ}$

$u \cos θ$

$\frac{u}{2} \sqrt{1 + 3 \cos^{2} θ}$

answer is B.

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Detailed Solution

$s = \sqrt{H^{2} + R^{2} / 4}$

$H = \frac{u^{2} \sin^{2} θ}{2 g}, R = \frac{u^{2} \sin 2 θ}{g}$

Average velocity $= \frac{S}{t} = \frac{S}{T / 2} = \frac{25}{T} = \frac{2 (\sqrt{H^{2} + {(\frac{R}{2})}^{2}})}{T}$

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