Question

A particle is projected at 60 to the horizontal with a kinetic energy KE. The kinetic energy at the highest point is:
\[
A.\,KE \\
B.\,Zero \\
C.\,\dfrac{{KE}}{4} \\
D.\,\dfrac{{KE}}{2} \\ \]

Answer 1

Hint: According to the law of conservation of energy, energy can neither be created nor be destroyed. It can only transform from one form into another form. Thus using the law, we will compare the loss of potential which is actually converted into the gain of kinetic energy and putting mass, the subject of the equation.

Complete step by step answer:
 The law of conservation of energy is written as follow; “In a closed system, that is, a system that is isolated from its surroundings, the total energy of the system is conserved.” In simple words, energy can neither be created nor destroyed; it can only be converted from one form to another.

Here, in our case, the particle is thrown at an angle of 60 degree with the horizontal. Thus, the particle when thrown must have an initial velocity and hence a particular kinetic energy which in our case is denoted by KE. After the particle is thrown, the acceleration due to gravity acts on the particle which decelerates the particle as the forces are in the opposite direction.

In this time, the particle’s potential energy increases as it gains a certain height and its kinetic energy decreases. When the particle reaches the highest point, its velocity becomes zero and it achieves the maximum height. Thus its potential energy is the maximum and its kinetic energy becomes zero.

Hence, option (B) is the correct answer.

Note:After reaching the highest point, the particle starts gaining kinetic energy but in the opposite direction. This energy is because of the acceleration due to gravity, as the gravitational force starts acting on the particle, its kinetic energy increases and the potential energy decreases and the potential energy becomes zero when the particle hits the ground.