Question

You carefully place a small rubber ball (mass m) on top of a much bigger basketball (mass M), and drop these from some height h. What is the velocity of the smaller ball after the basketball hits the ground, reverses direction, and then collides with the small rubber ball?

Answer 1

The velocity of the smaller ball after the basketball hits the ground, reverses direction, and then collides with the small rubber ball can be calculated using the principle of conservation of momentum.

Step-by-step explanation:

When the basketball collides with the ground, it will experience a change in momentum. Since momentum is conserved, the smaller rubber ball will also experience a change in momentum. This change in momentum will cause the smaller ball to gain velocity in the opposite direction of the basketball's motion.

The velocity of the smaller ball after it collides with the basketball can be calculated using the principle of conservation of momentum. The equation is:

m_1v_1 + m_2v_2 = m_1v'_1 + m_2v'_2

where m_1 and m_2 are the masses of the basketball and the smaller ball respectively, v_1 and v_2 are the velocities of the basketball and the smaller ball before the collision, and v'_1 and v'_2 are the velocities of the basketball and the smaller ball after the collision.

In this case, since the basketball is much bigger and more massive than the smaller ball, we can assume that the basketball's velocity approaches 0 after it collides with the ground. Therefore, we can simplify the equation to:

m_1v_1 + m_2v_2 = m_2v'_2

Rearranging the equation to solve for v'_2, we get:

v'_2 = \frac{m_1v_1 + m_2v_2}{m_2}

So, the velocity of the smaller ball after the basketball hits the ground, reverses direction, and then collides with the small rubber ball can be calculated using this equation. Plug in the known values for mass and velocity to find the answer.

Answer 2

3v

Step-by-step explanation:

A small rubber ball of mass m which is place at top of a bigger basket ball of mass M. These two balls are dropped from the same height h.

The velocity of the smaller ball will be 3v when the basketball hits the ground, reverses direction, and then collides with the small rubber ball.

Thus the answer is 3v.