The required energy depends on flag mass, gravitational acceleration and pole height. Raising it slowly or quickly does not change the work done. Doubling the lifting speed halves the time, doubling the required power.
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Lifting to the 20th floor requires twice the energy because the vertical height is doubled. However, since the time taken is also doubled, the power required remains exactly the same as before.
The gain in potential energy is 36250 joules in both cases, calculated by multiplying mass, gravity and height. Gravitational potential energy depends only on vertical height and is completely independent of the path taken.
Statements (iii) and (iv) are correct. At the highest peak, vertical velocity momentarily becomes zero making kinetic energy zero, while the entire initial mechanical energy turns into maximum gravitational potential energy at that height.
The correct filled terms are force and displacement for part one, one for part two, half m v square for part three, m g h for part four and rate for part five respectively.