First slide

Second law

Question

A ball of mass m is thrown upward with a velocity v. If air exerts an average resisting force F, the velocity with which the ball returns back to the thrower is

Moderate

A

$V \sqrt{(\frac{mg}{mg + F})}$
B

$V \sqrt{(\frac{F}{mg + F})}$
C

$V \sqrt{(\frac{mg - F}{mg + F})}$
D

$V \sqrt{(\frac{mg + F}{mg})}$

Solution

For upward motion, Retarding force = m g + F
$∴ Retardation a = \frac{mg + F}{m}$
$Distance s = \frac{V^{2}}{2 a} = \frac{V^{2} m}{2 (mg + F)}$
For downward motion, force = m g - F
$∴ Acceleration a^{'} = \frac{mg - F}{m}$
$Distance s^{'} = \frac{v^{' 2}}{2 a^{'}} = \frac{v^{' 2} m}{2 (mg - F)}$
$Since s^{'} = s, \frac{v^{' 2}}{mg - F} = \frac{v^{2}}{mg + F}$
$∴ v^{'} = v \sqrt{(\frac{mg - F}{mg + F})}$

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