A projectile is fired vertically up from the bottom of a crater (big hole) on the moon. The depth of the crater is R/100, where R is the radius of the moon. If the initial velocity of the projectile is the same as the escape velocity from the moon surface. The maximum approximate height attained by the projectile above the lunar (moon) surface is xR. Find value of x.
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(99)
Sol. speed of particle at A V A = escape velocity on the surface of moon = 
At highest point B, V B = 0
From energy conservation.
= m (V B – V A ) = m 
or 
, also, [3R 2 – r 2 ]
∴ 
or 
h = 
h = 
or h = 99.5 R ≈ 99R Ans
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