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A billiard ball initially at rest is given a sharp impules by a cue. The cue is held horizontally at a distance h above the centre line as in figure. The ball leaves the cue with a speed v and eventually acquires a speed 9/7 v. Show that h=4R/5, where R is the radius of the ball.
My attempt-
The friction force acts in the direction of motion as angular velocity is greater than linear speed (backward slipping occurs).considering rotation about central axis,fR=I(alpha) where (alpha) is the angular acceleration.I can get 2 equations relating linear speed at time t and angular speed at time t.But I don't know how to relate impulse with speed of the ball.I also wanted to ask that if we consider rotation about the point of contact, there is no torque acting on the sphere. How do we proceed this way?
linear impulse is integral of force w.r.t. time. it is equal to change in linear momentum. Angular impulse =
r X linear impulse =change in angular momentum
these two conditions will lead to the required equations
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