Final answer:
To find the force a 70 kg high jumper needs to exert to achieve an acceleration 4 times that of gravity, one must multiply the mass (70 kg) by four times the acceleration due to gravity (39.2 m/s²), resulting in a force of 2744 newtons.
Step-by-step explanation:
The question discusses a scenario where a high jumper with a mass of 70 kg needs to exert a force on the ground to achieve an upward acceleration of 4 times the acceleration due to gravity. To solve this problem, we need to use Newton's second law of motion which states that F = ma, where F is the force, m is the mass and a is the acceleration.
Firstly, we must calculate the acceleration. We know that acceleration due to gravity (g) is 9.80 m/s², therefore an acceleration 4 times this value would be a = 4g = (4)(9.80 m/s²) = 39.2 m/s². Now, we apply Newton's second law:
F = ma = (70.0 kg)(39.2 m/s²) = 2744 N
Therefore, the force the high jumper must exert on the ground is 2744 newtons (N).