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A sphere of mass m and radii r(a tennis ball) falls freely from a height of H and angular velocity(clockwise) about its axis omega.Coefficient of restitution is e

The coefficient of friction is mu.

After the sphere touches the ground it moves in the forward direction.

We have to find the range of the sphere.

Now we can find the velocities by energy conservation.

We we can apply angular conservation about the point which touches the ground.

initial translational + initial rotational = final translational + final rotational

Final velocity * e = Initial velocity.

Lets suppose that after collision the velocities of the sphere is vx and vy. so we have four variables final angular velocity,final velocity,Vx and Vy.

But we have just two equations. we can get one more by angular conservation which i am unable to get through and we are still one short.