Question

A boy of mass 40kg climbs a up a stairs to a height of 30m calculate the P. E if the boy falls from this heigt and find the v in which he hits the ground

Answer 1

PE = mgh = 40×10×30 = 12000 J

If he falls, entire PE is converted to KE.

$\frac{1}{2} m {v}^{2} = mgh \\ \\ {v}^{2} = \frac{2mgh}{m} \\ \\ {v}^{2} = 2gh \\ \\ v = \sqrt{2gh} \\ \\ v = \sqrt{2 \times 10 \times 30} = \sqrt{600} \\ \\ v = 10 \sqrt{6} \: \: m {s}^{ - 1}$

Answer 2

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PE = mgh = 40×10×30 = 12000 J

If he falls, entire PE is converted to KE.

$\frac{1}{2} m {v}^{2} = mgh \\ \\ {v}^{2} = \frac{2mgh}{m} \\ \\ {v}^{2} = 2gh \\ \\ v = \sqrt{2gh} \\ \\ v = \sqrt{2 \times 10 \times 30} = \sqrt{600} \\ \\ v = 10 \sqrt{6} \: \: m {s}^{ - 1}$

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