A body is projected up with a velocity equal to 3 4 th of the escape velocity from the surface of the earth. The height it reaches is (Radius of the earth =R )

Step-by-step solution

Velocity of projection v= 3 4 v_e where, v_e= escape velocity = 2 g R Maximum height attained by the body aligned h & = v^2 R 2 g R-v^2 & = ( 3 4 2 g R )^2 R 2 g R- ( 3 4 2 g R )^2 = 9 16 2 g R R 2 g R- 9 16 2 g R & = 9 16 2 g R^2 2 g R (1- 9 16 ) = 9 16 R 7 16 & = 9 7 R aligned