Question

A ball is thrown with initial kinetic energy 100j at an angle theta to the horizontal.if kinetic energy at the top is 25j then angle of projection?

Answer 1

Initial energy = 1/2 mu² = 100J …..........(1)

Where u = initial velocity with which it is thrown.

where m = mass of the ball.

At the top most point there is only horizontal component of velocity:

(ucosθ)

The vertical component will be zero.

So energy at the top most point will be :

= 1/2 mu²cos2θ = 30

=> 100cos2θ = 30 (using equation (1))

=> cosθ = √(30/100) = √(3/10)

=> θ=cos-1√(3/10)

√3/10 = 0.54772.

Cos ⁻¹ 0.54772 = 56.79°