Final answer:
The velocity of the 2.60 g ping-pong ball must be approximately 204.9 m/s to have the same kinetic energy as the 7.0 kg bowling ball.
Step-by-step explanation:
To find the speed at which the 2.60 g ping-pong ball must move to have the same kinetic energy as the 7.0 kg bowling ball, we can use the equation:
Kinetic Energy = 0.5 x mass x velocity2
For the bowling ball:
Kinetic Energybowling ball = 0.5 x 7.0 kg x (2.35 m/s)2
For the ping-pong ball:
Kinetic Energyping-pong ball = 0.5 x 0.0026 kg x (velocity of ping-pong ball)2
Set the two kinetic energies equal to each other and solve for the velocity of the ping-pong ball:
0.5 x 7.0 kg x (2.35 m/s)2 = 0.5 x 0.0026 kg x (velocity of the ping-pong ball)2
Simplifying, we get:
(velocity of the ping-pong ball)2 = (7.0 kg x (2.35 m/s)2) / 0.0026 kg
Taking the square root of both sides, we find that the velocity of the ping-pong ball must be approximately 204.9 m/s to have the same kinetic energy as the bowling ball.