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An object reaches a maximum vertical height of 23.0 m when thrown vertically upward on the earth. How high would it travel on the moon where the acceleration due to gravity is about one sixth that on the earth ? Assume that initial velocity is the same.

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100m

10m

69m

138m

answer is A.

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Detailed Solution

We now, maximum height for a vertically projected body is

$\begin{array}{l} h = \frac{u^{2}}{2 g} \Rightarrow h \propto \frac{1}{g}; \frac{h_{1}}{h_{2}} = \frac{g_{2}}{g_{1}} \\ \frac{h}{h_{2}} = \frac{g / 6}{g} \Rightarrow \frac{h}{h_{2}} = \frac{1}{6} \end{array}$
h₂ = 6h = 6 x 23 = 138 m

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