Question

A missile is launched with a velocity less than the escape velocity. The sum of its kinetic and potential energies is:
A) Positive
B) Negative
C) Zero
D) Maybe positive or negative depending upon its initial velocity

Answer 1

Hint: Recall the concept of escape velocity. Escape velocity is defined as the minimum velocity that is required by any system so that if it is projected upwards, it can overcome the gravitational pull of the planet. If an object has escape velocity, then it will not fall back to the planet or Earth.

Complete answer:
Kinetic energy is defined as the energy possessed by any body or system due to its motion. Since the missile will be moving, it will have some kinetic energy. Also, the direction of the missile launched is upward. So, it will also have some potential energy. This is because potential energy is the energy possessed by any body due to its height.
The sum of kinetic and potential energy will be negative. This is because if the velocity with which the missile is launched is less than escape velocity, then the missile is bound by the gravitational field of Earth. This results in negative total energy.

Option B is the right answer.

Note: It is important to remember that if an external force is applied on any system, then the position of the system or the object will change. As a result, the change in potential energy of the system is equal to the amount of work done on the object by the forces. Gravitational potential energy is the energy possessed by the object due to a change in its position when the object is present in the gravitational field.