Question

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? 

(A) Its speed is half of its initial speed. 

(B) Its kinetic energy is half of its initial kinetic energy. 

(C) Its potential energy is half of its initial potential energy. 

(D) Its total mechanical energy is half of its initial value. 

(E) Its total mechanical energy is half of its value at the highest point.

Answer 1

Correct option (B) Its kinetic energy is half of its initial kinetic energy.

Similar to the discussion above. Energy is conserved so the term mgh + ½ mv² must remain constant. As the object rises it loses K and gains U. Since the height is H/2 it has gained half of the total potential energy it will end up with which means it must have lost half of its kinetic energy, so its K is half of what it was when it was first shot.