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A missile is launched at an angle of 60^...

A missile is launched at an angle of `60^(@)` to the vertical with a velocity `sqrt(0.75 gR)` from the surface of the earth (R is the radius of the earth). Find its maximum height from the surface of earth. (Neglect air resistance and rotation of earth).

Text Solution

Verified by Experts

From conservation of mechanical energy
`(1)/(2)mv_(0)^(2)-(GMm)/(R )=(1)/(2)mv_(1)^(2)-(GMm)/(R+h)` ….(i)
Also from conservation of angular momentum
`mv_(0)R sin 60^(@) = mv_(1) (R+h)` ….(ii)
Solving (i) and (ii) and putting `v_(0) = sqrt((3GM)/(4R))`, we get
`h ~~ 0.25 R`.
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