A solid ball of radius 0.2 m and mass 1 kg is given an instantaneous impulse of 50 N-s at point P as shown. Find the number of rotations made by the ball about its diameter before hitting the ground. The ball is kept on smooth surface intially

Explanation

Impulse gives translational velocity
`u=("Impulse")/("Mass")` along impulse
`= 50 m//s`
T = time of flight of projectile
`= (2u sin theta)/(g)=(2xx50xxsin 60^(@))/(10)=5sqrt(3)s`
Impulse give angular impulse also
`omega=("Impulse" xx R)/(I) or omega=("Impulse" xxR)/((2)/(5)mR^(2))=625 "rad/s"`
Number of rotations, `n=(omegaT)/(2pi)=(3125 sqrt(3))/(2pi)`.