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A child is sitting on a swing. Its minimum and maximum heights from the ground are 0.75 m and 2 m respectively, its maximum speed will be
A
10 m/s
B
5 m/s
C
8 m/s
D
15 m/s
Detailed Solution
At the highest point the swing momentarily stops; at the lowest point the speed is maximum.
Apply conservation of mechanical energy between the maximum and minimum points:
$mgh = mgh_1 + \dfrac{1}{2}mV^2$
$V = \sqrt{2g(h - h_1)} = \sqrt{2 \times 10 \times (2 - 0.75)} = \sqrt{25}$
$V = 5$ m/s
Apply conservation of mechanical energy between the maximum and minimum points:
$mgh = mgh_1 + \dfrac{1}{2}mV^2$
$V = \sqrt{2g(h - h_1)} = \sqrt{2 \times 10 \times (2 - 0.75)} = \sqrt{25}$
$V = 5$ m/s