First slide

Release from certain height

Question

A stone is dropped from a height h. It hits the ground with a certain momentum P. If the same stone is dropped from a height 100% more than the previous height, the momentum when it hits the ground will change by:

Moderate

A

200%
B

100%
C

68%
D

41%

Solution

$P = mv = m \sqrt{2 gh} \Rightarrow P \propto \sqrt{h}$
$\frac{P_{2} - P_{1}}{P_{1}} \times 100 % = \frac{\sqrt{h_{2}} - \sqrt{h_{1}}}{\sqrt{h_{1}}} \times 100$
$= [\sqrt{\frac{h_{2}}{h_{1}}} - 1] \times 100 \{\sqrt{(\frac{200}{100})} - 1\} \times 100$
$= (\sqrt{2} - 1) \times 100 = 0 .414 \times 100 = 41 %$

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