If the body is projected vertically up with a velocity V, then the velocity of the body at half of the maximum height H is,( acceleration due to gravity=g)

by question ,velocity of projection =u=V; acceleration due to gravity=a=g; final velocity=V=0; displacement=maximum height⇒s=H  we know, V2=U2+2aS 0=V2+2(-g)H H=V22g---(1) to find, velocity=V=vmid point at s=H2;velocity of projection =u=V substitute in V2=U2+2aS v2mid point=V2+2(-g)(H2) substitute equation (1) v2mid point=V2-gV22g v2mid point=V2-V22 v2mid point=V22 square root both sides vmid point=V2