Question

a body is projected such that it's kinetic energy at the top is 3/4 of it's initial kinetic energy. what is the initial angle of projection

Answer 1

As there is no acceleration in the horizontal direction the velocity component will remain same as vcos∅ and at highest vertical component will be zero. so total velocity at top will be vcos∅

K.E will be 1/2 m (vcos∅)²

initial energy will be 1/2 mv²

at the highest point

K.E = 3/4 of initial K.E

1/2 m(vcos∅)² = 1/2 mv²× 3/4

∅= 30°