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A man projects a ball vertically up from the ground with kinetic energy K₁ such that when it reaches a height of 20 m, it has an upward velocity of 15 m/s. Next he throws the same ball vertically up from the ground with kinetic energy K₂ such that it just reaches the previous height of 20 m. The ratio K₁ : K₂ is (g = 10 m/s²)

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25 : 16

5 : 4

9 : 16

16 : 9

answer is A.

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Detailed Solution

$\frac{E_{1}}{E_{2}} = \frac{\frac{1}{2} {mv}^{2} + mgh}{mgh} = \frac{m (\frac{1}{2} v^{2} + gh)}{m gh} = \frac{\frac{1}{2} {(15)}^{2} + 10 \times 20}{10 \times 20} = \frac{25}{16}$

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