Final answer:
The average vertical force exerted on the jumper by the floor is equal in magnitude to the force the jumper exerts on the floor, which is calculated to be 3430 N based on Newton's third law of motion.
Step-by-step explanation:
The question pertains to the physical interaction between a high jumper and the floor during the jump process. Newton's third law states that for every action, there is an equal and opposite reaction. Therefore, the average vertical force exerted on the jumper by the floor will be equal in magnitude but opposite in direction to the force exerted by the jumper on the floor. Given that the body weight of the jumper is 993820 N and they exert a force of 17851640 N downwards, the floor must exert an equal force upwards to comply with Newton's third law.
To calculate the force, we use the equation:
Where:
- F is the force exerted by the floor on the jumper
- m is the mass of the jumper (body weight divided by gravitational acceleration)
- a is the upward acceleration of the jumper
- g is the acceleration due to gravity, which is 9.80 m/s²
Assuming the acceleration (a) is 4 times the acceleration due to gravity (given in a related problem), and the mass of the jumper is 70.0 kg (the force of gravity on the mass is 993820 N divided by 9.80 m/s²):
- F = (70.0 kg) * [(4 * 9.80 m/s²) + 9.80 m/s²]
- F = (70.0 kg) * [39.2 m/s² + 9.80 m/s²]
- F = (70.0 kg) * 49.0 m/s²
- F = 3430 N
Thus, the average vertical force exerted on the jumper by the floor is also 3430 N.