Final answer:
The rebounding dodgeball would deliver a greater change in momentum than the dodgeball that sticks to the opponent, as it involves a change in velocity in opposite directions, effectively doubling the change compared to when the dodgeball stick and the velocity goes to zero.
Step-by-step explanation:
To determine which would deliver a greater change in momentum to an opponent’s body, we need to compare the scenarios involving a dodgeball that travels at 10 m/s and either rebounds or sticks to the person. Momentum, given by the product of mass and velocity, changes when a force is applied over time. For an elastic collision, where the ball rebounds at the same speed but in the opposite direction, the change in momentum is greater because the velocity change involves two speeds in opposite directions. In contrast, when a ball sticks to a person, the change in momentum involves only the initial speed slowing to zero.
If the mass of the dodgeball is m and its initial velocity is v (10m/s) and final velocity after rebounding is -v, the change in momentum (Δp) is given by:
Δp = m * (-v) - m * v = -2m * v
For the case where the ball sticks, the change in momentum is:
Δp = m * 0 - m * v = -m * v
It is clear from the equations that the ball which rebounds imparts a larger change in momentum equivalent to double the product of the mass and velocity compared to the ball that sticks. Hence, the rebounding dodgeball would deliver a greater change in momentum than the dodgeball that sticks. Note: This discussion assumes a perfectly elastic collision in the case of rebound and an inelastic one for the sticking scenario.