Question

The potential energy of a projectile at maximum height is 3/4 times kinetic energy of projection. Its angle of projection is

1) 30°
2) 45°
3) 60°
4) none​

Answer 1

Potential energy at the highest point = mgh

Kinetic energy at the highest point = 1/2 mv²

Now, as per question.....

P.E. = (3/4) K.E.

mgh = (3/4) mv²/2

[Height of Projectile = v²sin²Ø/2g]

g(v²sin²Ø)/2g = (3/8)v²

sin²Ø/2 = 3/8

sin²Ø = 3/4

sinØ = √3/2

sinØ = sin 60°

Ø = 60°

Henceforth,

The angle of Projection of particle = Ø = 60°