An exceptional standing jump would raise a person 0.80 m off the ground. To do this, the person must first lower himself about 0.20 m prior to jumping. What force must a 70‒kg person, ready to jump at this position, exert against the ground in order to reach that height and raise himself a total distance of 1.00 m?
To calculate the force required for the person to accomplish the jump, we can use the work-energy principle.
The work-energy principle states that the work done on an object is equal to the change in its kinetic energy. In this case, we need to calculate the work done against gravity to raise the person to a height of 0.80 m.
The work done against gravity can be calculated using the formula:
Work = Force * Distance * cosθ
In this case, the distance is the total distance the person raises themselves, which is 1.00 m, and the angle θ between the upward force and the displacement is 0° (since the force and displacement are in the same direction).
Therefore, the work done against gravity is:
Work = Force * 1.00 m * cos(0°)
Since cos(0°) = 1, the equation simplifies to:
Work = Force * 1.00 m
According to the work-energy principle, this work is equal to the change in potential energy of the person:
Work = Change in Potential Energy
The change in potential energy can be calculated using the formula:
Change in Potential Energy = m * g * Change in Height
Where:
m = mass of the person (70 kg)
g = acceleration due to gravity (9.8 m/s^2)
Change in Height = 0.80 m (the height the person jumps)
Therefore, the equation becomes:
Force * 1.00 m = 70 kg * 9.8 m/s^2 * 0.80 m
Simplifying further:
Force = (70 kg * 9.8 m/s^2 * 0.80 m) / 1.00 m
Finally, calculating the force:
Force = 549.6 N
So, the person must exert a force of 549.6 N against the ground to reach a height of 0.80 m and raise themselves a total distance of 1.00 m.