Question

If the maximum height attained by a projectile is equal to maximum horizontal range of another projectile , then what is the ratio of their velocities of projection

Answer 1

Range of a projectile is given by the formula

R=v2sin(2θ)g

While maximum height of a projectile is given by

H=u2sin2(θ)2g

Per the requirements of the question, R=H, therefore

v2sin(2θ1)gv2sin(2θ1)v2u2vu=u2sin2(θ2)2g=u2sin2(θ2)2=sin2(θ2)2sin(2θ1)=sin(θ2)2sin(2θ1)−−−−−−−−√