Question

A ball is projected vertically upwards with kinetic energy $E$. The kinetic energy of the ball at the highest point of its flight will be:
(A). $E$
(B). $\dfrac{E}{\sqrt{2}}$
(C). $\dfrac{E}{2}$
(D). zero

Answer 1

Hint: When a ball is projected upwards, it is under the action of force of gravity. Therefore, the gravity does work on it due to which it possesses potential energy and the kinetic energy is due to its motion. The sum of kinetic energy and potential energy is called mechanical energy and it is conserved for the system of the ball.

Complete answer:
When the ball is in motion it possesses kinetic energy. Kinetic energy is the property of a moving body which depends on its velocity as well as its motion. It is given by-
$E=\dfrac{1}{2}m{{v}^{2}}$
Here, $E$ is the kinetic energy
$m$ is the mass of the moving body
$v$ is the velocity
When a body is moving opposite to the force of gravity, the Earth does work on the body, due to which the potential energy of the body increases. The potential energy is the energy stored in a body by virtue of its position. It is given by –
$U=mgh$
Here, $U$ is the potential energy
$g$ is acceleration due to gravity
$h$ is the height of the body
The mechanical energy is the sum of kinetic energy and potential energy of a body and it is always constant.
Given that the ball is thrown upwards, as it goes up its kinetic energy decreases and potential energy increases. At the highest point the total kinetic energy is converted into potential energy and hence the kinetic energy becomes zero.
Therefore, at the highest point, the kinetic energy becomes zero.

Hence, the correct option is (D).

Note:
When the ball is thrown upwards only force of gravity acts on it so its acceleration is constant. Mechanical energy for the ball is conserved because force of gravity is a conservative force that means it depends on the initial and final state of the ball and not the path taken by it.