First slide

Projection Under uniform Acceleration

Question

A particle is projected from the ground with an initial speed of v at an angle $θ$ with horizontal. The average velocity of the particle between its point of projection and highest point of trajectory is:

Moderate

A

$\frac{v}{2} \sqrt{1 + 2 \cos^{2} θ}$
B

$\frac{v}{2} \sqrt{1 - 4 \cos^{2} θ}$
C

$\frac{v}{2} \sqrt{1 + 3 \cos^{2} θ}$
D

$v cosθ$

Solution

Average velocity = $\frac{Displacement}{Time}$
$v_{av} = \frac{\sqrt{H^{2} + \frac{R^{2}}{4}}}{\frac{T}{2}} - - - - (i)$
Here, H = maximum height = $\frac{v^{2} \sin^{2} θ}{2 g}$
R = range = $\frac{v^{2} \sin 2 θ}{g}$
and T = time of flight = $\frac{2 v sinθ}{g}$
$v_{av} = \frac{v}{2} \sqrt{1 + 3 \cos^{2} θ}$

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