Two skaters A and B, both of mass 70 kg, are approaching one another over a frictionless fixed surface, each with a speed of 1 m/s with respect to the surface. A carries a bowling ball of mass of 10 kg. Both skaters can throw the ball at 5 m/s relative to themselves. To avoid collision they start throwing the ball back and forth when they are 10 m apart. How many minimum number of throws are required?
Physics · Mixed Chapter
JEE Mains

Question

Two skaters A and B, both of mass 70 kg, are approaching one another over a frictionless fixed surface, each with a speed of 1 m/s with respect to the surface. A carries a bowling ball of mass of 10 kg. Both skaters can throw the ball at 5 m/s relative to themselves. To avoid collision they start throwing the ball back and forth when they are 10 m apart. How many minimum number of throws are required?

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: On a frictionless surface, only exchanging momentum by throwing the ball can change skaters’ approach velocities. The ball is initially held by A. Step 2: When A throws the ball towards B at 5 m s⁻¹ relative to A, A recoils, reducing A’s forward velocity. B catches the ball, exchanging momentum. Step 3: B then throws the ball back toward A, producing a further recoil in the opposite direction. The impulse exchange is sufficient to prevent their initial approach, so the minimum is two th…