Momentum conservation gives:
velocity of the two carts after collision
Consider the circular motion of the ball atop the cart if it were stationery. If at the lowest and highest points the ball has speeds and , respectively, then
where is the tension in the string when the ball is at the highest point.
The smallest is given by .
The smallest is given by
When the cart is moving, is the velocity of the ball relative to the cart. As the ball has initial velocity, velocity of the ball relative to the cart after the collision is . Hence, the smallest velocity for the ball to go round in a circle after the collision is given by: