Final answer:
The ping-pong ball must move at a speed of 16752.757 m/s to have the same momentum as a bowling ball of mass 8.7 kg moving at 3.84 m/s.
Step-by-step explanation:
To calculate the speed at which the ping-pong ball must travel to have the same momentum as the bowling ball, we can use the conservation of momentum principle, which states that the momentum before an event must equal the momentum after the event, provided no external forces act upon them. In this case, we want to find the velocity that gives the ping-pong ball the same momentum as the bowling ball at 3.84 m/s.
The momentum of an object is given by the equation p = m × v, where p is the momentum, m is the mass, and v is the velocity. For the bowling ball, the momentum (pbowl) is 8.7 kg × 3.84 m/s, which equals 33.408 kg·m/s.
The mass of the ping-pong ball needs to be converted from grams to kilograms: 1.994 g = 0.001994 kg. To find the velocity needed for the ping-pong ball to match the bowling ball's momentum, we solve for v in the equation p = m × v using the bowling ball's momentum (pbowl) and the mass of the ping-pong ball (mpong):
vpong = pbowl / mpong
vpong = 33.408 kg·m/s / 0.001994 kg
vpong = 16752.757 m/s
Therefore, the ping-pong ball must move at a speed of 16752.757 m/s to have the same momentum as the bowling ball moving at 3.84 m/s.