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

68%

41%

200%

100%

Solution

41%

velocity space straight v space equals space square root of 2 gh end root space space space space space space space.... left parenthesis straight i right parenthesis and space momentum space straight p space equals space mv space space space space... space left parenthesis ii right parenthesis From space left parenthesis Eqs. right parenthesis space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis comma space we space have space straight p proportional to square root of straight h Here comma straight p subscript 2 over straight p subscript 1 space equals space square root of straight h subscript 2 over straight h subscript 1 end root therefore space fraction numerator straight p subscript 2 over denominator straight p subscript 1 space end fraction space equals square root of fraction numerator 2 straight h over denominator straight h end fraction space end root space equals square root of 2 straight p subscript 2 space equals 1.414 straight p subscript 1 percent sign change space equals space fraction numerator straight p subscript 2 minus straight p subscript 1 over denominator straight p subscript 1 end fraction space straight x space 100 space equals space 41 percent sign

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