Final answer:
The question deals with trampoline safety and the physics forces at play, such as the force required for a trampoline to accelerate a 45.0-kg gymnast upwards at 7.50 m/s², which is 337.5 Newtons.
Step-by-step explanation:
The number of jumpers allowed on the trampolines at any given time may not be explicitly noted in these sections, but it's clear that safety and the forces involved while using a trampoline are key considerations. When discussing safety and physics in trampolining, recognizing the importance of factors such as force, acceleration, and mass is crucial.
For instance, the force a trampoline must apply to a 45.0-kg gymnast to achieve an upward acceleration of 7.50 m/s² is calculated by using Newton's second law, which states that force equals mass times acceleration (F = ma).
For the 45.0-kg gymnast mentioned, the force would be:
F = m × a
F = 45.0 kg × 7.50 m/s²
F = 337.5 N (Newtons)
Therefore, the trampoline needs to exert a force of 337.5 Newtons on the gymnast. This application of force is necessary regardless of whether the gymnast is moving up, down, or is stationary because force is needed to change the velocity of any mass.
This principle directly translates to professional applications in sports and safety planning, such as ensuring athletes train safely and effectively.