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).

A missile is launched at an angle of 60^(@) to the vertical with a vel

1.	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).
Answer» Solution :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`.