This problem is from one of my practice papers for the JEE , the situation of a freely falling rotating ball which collides with the ground twice.

Question asks for the horizontal distance covered between the first two collisions .

Coefficient of restitution , coefficient of friction , mass and moment of inertia of a ball are given.

enter image description here

During the collision of the ball with the ground , normal reaction force is impulsive , since normal reaction is huge at that instant - friction also has to be huge - meaning it has to be impulsive .If friction is huge , then the lowest point of the ball has to come to rest during the course of collision.

I've tried all this numerically , which give me a wrong answer which questions the assumption "Is friction impulsive in this case"

Is my calculation wrong enter image description here

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    $\begingroup$ Yes, the problem can be adequately handled by using impulse. Can you show your calculation? $\endgroup$ – netflix_and_physics Jun 8 at 19:46
  • $\begingroup$ @netflix_and_physics yes , added my calculation $\endgroup$ – Fallen Grenade Jun 9 at 4:27
  • $\begingroup$ Since the coefficient of restitution is 0.5 the ball will bounce back, and friction won't act till the ball is at rest. $\endgroup$ – netflix_and_physics Jun 9 at 7:57
  • $\begingroup$ How can you justify this assumption? Since you can calculate the impulse due to friction, you can find out the final angular velocity and see if the point comes at rest or not. $\endgroup$ – netflix_and_physics Jun 9 at 9:19
  • $\begingroup$ "Since the coefficient of restitution is 0.5 the ball will bounce back, and friction won't act till the ball is at rest" how do you know the time taken for collision and time taken by to get ball to rest. $\endgroup$ – Fallen Grenade Jun 9 at 9:20

Although you can apply angular impulse equation in this problem, personally i dont think its required. You see the question only asks you to find the horizontal distance, whih requires us to find only the horizontal translation velocity, as for the fact that why is rotation then involvd in this question , i believe rotation has been involved only so that a kinetic friction acts horizontally an pushes the ball forward. Here is the solutionenter image description here

enter image description here

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    $\begingroup$ The solution seems to use the right methods but is missing some subtleties. Can you write in Latex? It would be easier to read and edit. $\endgroup$ – netflix_and_physics Jun 9 at 9:03

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