Question

A ball of mass 0.50 kg is rolling across a table top with a speed of 5.0 m/s. When the ball reaches the edge of the table, it rolls down an incline onto the floor 1.0 meter below (without bouncing). What is the speed of the ball when it reaches the floor?

Answer 1

The speed of the ball when it reaches the floor is approximately 4.43 m/s.

Step-by-step explanation:

To find the speed of the ball when it reaches the floor, we need to consider conservation of energy. The potential energy of the ball at the top of the incline is equal to its kinetic energy at the bottom of the incline. The potential energy is given by mgh, where m is the mass of the ball (0.50 kg), g is the acceleration due to gravity (9.8 m/s²), and h is the height of the incline (1.0 m). The kinetic energy is given by (1/2)mv², where v is the speed of the ball at the bottom of the incline. Setting the potential energy equal to the kinetic energy and solving for v, we get:

v = sqrt(2gh)

Plugging in the values, we find:

v = sqrt(2 * 9.8 * 1.0)

v = sqrt(19.6)

v ≈ 4.43 m/s