An object is projected vertically upward from ground level. It rises to a maximum height H. If air resistance is negligible, which of the following must be true for the object when it is at a height H/2?

Explanation

In the absence of air resistance, the total mechanical energy of the object is conserved, which means it remains constant throughout the object's motion. The total mechanical energy is the sum of kinetic energy (K) and potential energy (U). Initially, at ground level, the object has maximum kinetic energy and zero potential energy. As it rises, it loses kinetic energy and gains potential energy.When the object reaches a height of H/2, it has gained half of the maximum potential energy it will achieve at height H. Consequently, it must have lost half of its initial kinetic energy to maintain the conservation of total mechanical energy. Therefore, the correct statement is that its kinetic energy is half of its initial kinetic energy.Option A is incorrect because speed is not directly halved at half the maximum height. Option C is incorrect because the initial potential energy is zero, and potential energy at any height is measured from that initial state. Option D is incorrect because the total mechanical energy remains constant, not halved.