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The maximum vertical distance through which a fully dressed astronaut can jump on 
the earth is 0.5 m. If mean density of the moon is two thirds that of the earth and 
radius is one quarter that of the earth, the maximum vertical distance through which 
he can jump on the moon and the ratio of time of duration of the jump 

Asked by rushikeshyeole21 1st February 2018, 4:58 PM
Answered by Expert
Answer:
The required equation to solve this problem :-   v2 = u2-2gh .  v is final speed in this case it is zero, when astronaut jumps and reaches maximum height his speed is zero. u is initial jumping speed. g is acceleration due to gravity and h is the maximum jumping height.
 
If jumping speed on earth and moon are assumed as same, then height is inversely proportional to acceleration due to gravity.
 
begin mathsize 12px style h proportional to 1 over g end style
now acceleration due to gravity begin mathsize 12px style g space equals space fraction numerator G M over denominator R squared end fraction space equals space G over R squared 4 over 3 pi R cubed rho space equals space G 4 over 3 pi R rho end style
G - gravitational constant M mass of earth, ρ is mean density, R is radius
 
If we consider 2/3 of earth density as moon's density and 1/2 of earth radius as moon's radius 
then acceleration due to gravity on moon, begin mathsize 12px style g subscript M space equals 1 over 6 g subscript E end style
gE is acceleration due to gravity on earth
 
begin mathsize 12px style fraction numerator j u m p i n g space h e i g h t space o n space M o o n over denominator j u m p i n g space h e i g h t space o n space E a r t h end fraction space equals space g subscript E over g subscript M space equals space fraction numerator g subscript E over denominator open parentheses begin display style bevelled 1 over 6 end style close parentheses begin display style begin display style g end style subscript E end style end fraction space equals space 6 end style
Hence the astronaut will jump a height of 6 × 0.5 = 3 m on moon
Answered by Expert 1st February 2018, 6:01 PM
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