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Q.
At her maximum height, a girl in a swing is 3 m above the ground and at the lowest point, she is 2 m above the ground. What is her maximum velocity?
Work, Energy and Power
Solution:
At the highest point, $v = 0, h_1 = 3 \,m$
$\therefore $ Total energy, $E_1 = mgh_1 + 0$
At the lowest point, $v = ?, h_2 = 2\,m$
Total energy, $E_{2}=mgh_{2}+\frac{1}{2}m\upsilon^{2}$
According to the law of conservation of energy, $E_{2} = E_{1}$
$mgh_{2}+\frac{1}{2}m\upsilon^{2}=mgh_{1}$
$\upsilon=\sqrt{2g\left(h_{2}-h_{1}\right)}$
$=\sqrt{2\times9.8\left(3-2\right)}$
$\upsilon=\sqrt{19.6}\,m\,s^{-1}$