Final answer:
To find the ball's speed immediately after it bounces, we calculate the potential energy at its maximum bounce height and equate it to kinetic energy, which allows us to solve for the speed.
Step-by-step explanation:
To determine the ball's speed immediately after it bounces, we can use the principles of energy conservation. The kinetic energy of the basketball just before hitting the ground will partly convert into potential energy at the peak of its bounce. Knowing that the ball reaches a maximum height of 32 cm after the bounce, we can calculate the potential energy at that height and then find the speed at which the ball left the ground right after the bounce.
Gravitational potential energy (PE) at maximum height (h) is given by PE = mgh, where m is the mass of the ball, g is the acceleration due to gravity (9.81 m/s2), and h is the height. Using h = 32 cm = 0.32 m, m = 0.625 kg, we get PE = 0.625 kg × 9.81 m/s2 × 0.32 m.
Since the potential energy at the height of 32 cm is equal to the kinetic energy (KE) just after the ball bounces, and KE is given by ½mv2, we can solve for v, the speed just after the bounce:
PE = KE
0.625 kg × 9.81 m/s2 × 0.32 m = ½ × 0.625 kg × v2
Solving for v gives us the speed immediately after the ball bounces.