Question

What is angle when range and height of projectile motion is same?

Answer 1

Let angle of projection is ∅ for which horizontal range and maximum height of a projectile are equal. and u is the intial velocity .

we know,

Maximum Height H = u²sin²∅/2g

horizontal range R = u²sin2∅/g

A/C to question, H=R

So, u²sin²∅/2g = u²sin2∅/g

[ using, sin2x = 2sinx.cosx ]

sin²∅/2 = 2sin∅.cos∅

tan∅ = 4

∅ = tan-¹( 4) or 75.96 degree

angle of projection = tan-¹(4) Ans.