First slide

Projection Under uniform Acceleration

Question

From a point on the ground a particle is projected with initial velocity u, such that its horizontal range is maximum. The magnitude of average velocity during its ascent is

Moderate

A

$\frac{{\sqrt 5 u}}{2}$
B

$\frac{{\sqrt 5 u}}{2\sqrt{2}}$
C

$\frac{5 u}{2\sqrt{2}}$
D

$\frac{{\sqrt 2 u}}{\sqrt{5}}$

Solution

$\large {V_{avg}} = \frac{{Total\,\,displacement(r)}}{{{t_a}}}$

$\large = \frac{{\frac{{{u^2}}}{{2g}}\sqrt {1 + \frac{1}{4}} }}{{u/\sqrt 2 g}}$
$\large = \frac{u}{{\sqrt 2 }}\frac{{\sqrt 5 }}{2}$
$\large = \frac{{\sqrt 5 u}}{{2\sqrt 2 }}$

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