Question

If range and height of a projectile are equal then find the angle of projection with the horizontal

Answer 1

Let θ be the angle of projection for which horizontal range and maximum height of a projectile are equal.Now,

H= u2 sin2 θ / 2g

R = u2 sin2θ / g

So, if H=R

then , u2 sin2 θ / 2g = u2 sin2θ / g

or, sin2 θ / 2 = sin2θ

or, sin2 θ  =  2 (2 sinθ  cosθ )

or tan θ = 4

or, θ  = tan -1 ( 4)