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Answer :
Either one of the given values is incorrect or there is some inconsistency in the problem statement.
To calculate the change in height of the in-line skater, we can use the work-energy principle, which states that the net work done on an object is equal to the change in its kinetic energy:
Net work = ΔK = (1/2)mvf^2 - (1/2)mvi^2
Here, ΔK is the change in kinetic energy, mvf and mvi are the final and initial velocities of the skater, and m is the mass of the skater.
The net work done on the skater can be calculated by summing the work done by external forces on the skater. Here, the skater does positive work of +4,819 J by pushing against the ground with his skates, while friction does negative work of -577 J. Therefore, the net work done on the skater is:
Net work = 4,819 J - 577 J = 4,242 J.
Substituting the given values in the equation for ΔK:
4,242 J = (1/2) x 73.0 kg x (1.70 m/s)^2 - (1/2) x 73.0 kg x (3.00 m/s)^2
This simplifies to:
4,242 J = -939.6 J
However, this is impossible since the net work cannot be negative while the initial and final speeds are both positive. Therefore, either one of the given values is incorrect or there is some inconsistency in the problem statement.
Without being able to solve the problem as stated, we cannot calculate the skater's change in height.
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