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Q. A girl in a swing is $2.5\, m$ above ground at the maximum height and at $1.5 \,m$ above the ground at the lowest point. Her maximum velocity in the swing is ($g$ = $10\, ms^{-2}$)

KEAMKEAM 2012Work, Energy and Power

Solution:

In this case,
Change in Potential energy = Kinetic energy
$\frac{1}{2} m v^{2} =m g\left(h_{2}-h_{1}\right) $
$v^{2} =2 g(2.5-1.5) $
$v^{2} =2 \times 10 \times 1$
$v =\sqrt{5 \times 2 \times 2} $
$v =2 \sqrt{5} m / s$