Final answer:
To match the kinetic energy of a 6.67 kg bowling ball moving at 2.23 m/s, a 2.26 g ping-pong ball must move at approximately 121.02 m/s.
Step-by-step explanation:
The question asks us to find the velocity at which a ping-pong ball must move so that it has the same kinetic energy as a moving bowling ball. To solve this, we use the formula for kinetic energy: KE = (1/2)mv², where 'm' is mass and 'v' is velocity.
First, let's calculate the kinetic energy of the bowling ball:
- KEbowling = (1/2) × 6.67 kg × (2.23 m/s)² = 16.57 J (rounding off to two decimal places)
Next, we need to set this equal to the kinetic energy of the ping-pong ball and solve for the velocity:
- (1/2) × 2.26 g × v² = 16.57 J
- Since we need the mass in kilograms, we convert 2.26 g to kg: 2.26 g = 0.00226 kg
- (1/2) × 0.00226 kg × v² = 16.57 J
- v² = (16.57 J) / (1/2 × 0.00226 kg)
- v² = 14646.02 m²/s²
- v = √(14646.02 m²/s²)
- v ≈ 121.02 m/s (rounding off to two decimal places)
Therefore, the ping-pong ball must move at approximately 121.02 m/s to have the same kinetic energy as the given bowling ball.