A 500 newton ballerina did 250 joules of work to lift herself upward through the air. She landed a total of 2.5 meters to the left after completing...

The ballerina weighing 500 N jumped up through the air and landed 2.5 m to the left of where she started. The work done by her in this was 250 J.

Work is equal to the product of force and displacement. The ballerina only does work in moving upwards as the gravitational force, which is equal to her weight, is acting downwards.

As she did 250 J of work, the maximum height reached by her in the jump is equal to 250/500 = 0.5 m. She landed 2.5 m to the left as she did not jump vertically upwards, rather she jumped at an angle approximately 21.8 degrees to the horizontal.

Once the ballerina has reached the maximum height, she is pulled down due to the force of gravity. There is no change in potential energy of the ballerina once she has come down. But she cannot recover the energy spent when she comes down.