An exceptional standing jump would raise a person 0.90 m off
the ground. To do this, what force must a person of mass 66 kg
exert against the ground? Assume the person crouches a distance
of 0.20 m prior to jumping, and thus the upward force has this
distance to act before he leaves the ground.
To find the force a person must exert against the ground to achieve a standing jump of 0.90 m, we need to use the principle of conservation of energy.
First, let's calculate the gravitational potential energy at the highest point of the jump. The formula for gravitational potential energy is given by:
PE = m * g * h
Where:
PE is the potential energy,
m is the mass of the person (66 kg),
g is the acceleration due to gravity (9.8 m/s^2),
and h is the height reached (0.90 m).
Substituting the given values into the formula, we have:
PE = 66 kg * 9.8 m/s^2 * 0.90 m
PE = 581.4 J
Next, let's calculate the work done by the person to achieve this jump. The work done is equal to the force applied multiplied by the distance over which the force is applied. In this case, the person crouches a distance of 0.20 m before jumping, so the upward force has this distance to act. The work done is given by:
W = F * d
Where:
W is the work done (equal to the potential energy),
F is the upward force,
and d is the distance over which the force is applied (0.20 m).
Substituting the values, we have:
581.4 J = F * 0.20 m
Now, we can solve for the upward force:
F = 581.4 J / 0.20 m
F = 2907 N
Therefore, a person of mass 66 kg must exert a force of 2907 N against the ground to achieve a standing jump of 0.90 m.