Question

The vertical distance through which a fully dressed astronaut can jump on the earth is 0.7m estimate the maximum vertical distance through which she can jump on a planet which has a mean density 5/9 times that of the earth and radius one quarter that of the earth

Answer 1

The astronaut will jump a height of 6 × 0.5 = 3 m on moon

Explanation:

Correct statement:

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.

Solution:

If jumping speed on earth and moon are assumed as same, then height is inversely proportional to acceleration due to gravity.

h∝1/g

Now acceleration due to gravity.

g = GM/R^2  = G/R^2 . 4/3πr^3ρ = G4/3πRρ

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:

gM = 1/6 gE

gE is acceleration due to gravity on earth

Jumping height on moon/ jumping height on earth = gE/gM

                     = gE/(1/6)gE = 6

The astronaut will jump a height of 6 × 0.5 = 3 m on moon

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