Question

Which of the following has both kinetic energy and potential energy?
A. A flying bird
B. A bent bow about to shoot an arrow
C. An athlete running at full speed
D. None of the above

Answer 1

Hint: Recall that kinetic energy is the energy possessed by a body when it is moving and potential energy is the energy possessed by a body when it is at rest. Think of which of the options have bodies both at rest and motion at the same time. It would help if the state of rest is treated relative to the ground, and the state of motion just as it is. In other words, gravitational force experienced by a body changes with vertical height but remains the same horizontally.

Formula Used:
Potential energy is generally measured as: $PE = mgh$, where m is the mass of the body, g is the acceleration due to gravity and h is the height or position of the body from the ground.
Kinetic energy is given as: $KE = \dfrac{1}{2}mv^2$, where m is the mass of the body and v is the velocity with which the body moves.

Complete answer:
Let us begin by understanding what kinetic and potential energies are and in what context we will be looking at them here.
We know that energy in a body can be stored in different forms. Work is performed by the body by utilizing this energy.
Now, when a body is at rest but has a potential to move, the energy possessed by it is called potential energy (PE). Note that the state of rest of the body is defined relative to another body. Potential energy is generally measured as: $PE = mgh$, where m is the mass of the body, g is the acceleration due to gravity and h is the height or position of the body from the ground. Thus, when an object is raised from the ground, work is done against gravity and the body possesses potential energy
However, the energy released by a body when it is in a state of motion is called kinetic energy (KE). Note that the state of motion of the body is independent of any other body and is hence defined non-relatively. Kinetic energy is given as: $KE = \dfrac{1}{2}mv^2$, where m is the mass of the body and v is the velocity with which the body moves.
Therefore, the PE is the energy possessed by a body by virtue of its position and KE is the energy possessed by a body by virtue of its motion.
Now, in the context of the question we see that:
1. A bent bow about to shoot an arrow can be looked at as an arrow which is currently at rest but has the potential to move when the string of the bow is released. Thus, the arrow possesses a potential energy.
2. An athlete running at full speed can be looked at as an athlete in a state of motion. Thus, the energy that an athlete expends is kinetic energy.
3. However, when we look at a flying bird, we see that firstly, it is at a height from the ground, which means that it is subjected to a gravitational potential, which is the work it does against the gravitational force to maintain its height, and secondly it is flying, which means it is in a state of motion, by virtue of which it possesses kinetic energy. Thus, The flying bird possesses both kinetic and potential energy.

The correct choice would hence be: A. A flying bird.

Note:
Remember that KE is measured at the point in space where a body is at the time of measurement, whereas PE is measured at the relative position of the body at the time of measurement.
Also, PE and KE can be interconverted to execute characteristic motion. For example, when a body is projected upwards, it moves upwards by utilizing the KE from the launch velocity and all the work that the body does against gravity gets stored as PE, and as the body begins to fall back to the ground, this PE is converted to KE.