First slide

Numericals based on work energy theorem

Question

A ball of mass m is thrown vertically up in air from the ground with initial speed u and is found to return to the starting point with a lesser speed of v. If g is the acceleration due to gravity, the maximum height reached by the ball is

Moderate

A

$\frac{u^{2}}{2 g}$
B

$\frac{v^{2}}{2 g}$
C

$\frac{u^{2} + v^{2}}{2 g}$
D

$\frac{u^{2} + v^{2}}{4 g}$

Solution

$e n e r g y l o s s b y t h e b a l l = \frac{1}{2} m (u^{2} - v^{2}) = 2 m g h h i s t h e h e i g h t l o s s d u e r e s i s t i v e f o r c e h = \frac{u^{2} - v^{2}}{4 g} s o h e i g h t i t h a s r e a c h e d \frac{u^{2}}{2 g} - h = \frac{u^{2}}{2 g} - (\frac{u^{2} - v^{2}}{4 g}) = \frac{u^{2} + v^{2}}{4 g}$

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