Final answer:
The speed of the ball relative to the player is calculated using the work-energy principle, where the work done equals the change in kinetic energy. With the values given, the speed is found to be approximately 8.5 m/s, making option c. the correct answer.
Step-by-step explanation:
The question asks for the calculation of the speed of the basketball relative to the player as it leaves his hand after the player has done work on it. To find the speed of the ball, we utilize the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy.
The work-energy principle is defined as:
Work (W) = Δ Kinetic Energy (KE) = KE_{final} - KE_{initial}
Since the ball starts from rest relative to the player, its initial kinetic energy is zero. Thus, the work done on the ball is equal to its final kinetic energy. The final kinetic energy of the ball can be expressed as:
KE_{final} = ½ m v^2
Where m is the mass of the ball and v is the speed of the ball relative to the player. Rearranging the formula to solve for the speed of the ball, we get:
v = √(2W/m)
Plugging in the known values gives us:
v = √(2 × 20.0 J / 0.56 kg)
v = √(71.4286)
v ≈ 8.5 m/s
Therefore, the correct option for the speed of the ball relative to the player as it leaves his hand is c. 8.5 m/s.