Question

Two objects with the same mass and same speed, but moving in opposite directions, have the same kinetic energy. Explain why this is true. A. Kinetic energy changes as an object falls in a gravitational field. B. Kinetic energy has units of joules. C. Kinetic energy is a scalar quantity that depends only on the speed but not direction of velocity. D. It is false. The two objects have opposite kinetic energies

Answer 1

The same mass and speed objects moving in opposite directions have the same kinetic energy because kinetic energy depends only on the speed but not the direction of velocity.

Step-by-step explanation:

The correct answer is C. Kinetic energy is a scalar quantity that depends only on the speed but not direction of velocity.

Kinetic energy is the energy of an object due to its motion. It depends on the object's mass and its velocity, and it is calculated using the formula K.E. = 1/2 * mass * velocity². Since the formula only includes the speed (magnitude of velocity) and not the direction of velocity, objects with the same mass and same speed, but moving in opposite directions, will have the same kinetic energy.

For example, if two objects both have a mass of 2 kg and are moving at a speed of 10 m/s, one in the positive x-direction and one in the negative x-direction, their kinetic energies will be the same:

K.E. object A = 1/2 * 2 kg * (10 m/s)² = 100 J

K.E. object B = 1/2 * 2 kg * (10 m/s)² = 100 J

Answer 2

We are given that two objects of same mass have the same velocity but in opposite directions. The kinetic energy of each object is given by:

`K=(1)/(2)mv^2`

Where:

`\begin{gathered} m=\text{ mass} \\ v=\text{ magnitude of velocity} \end{gathered}`

Since the kinetic energy depends on the mass and the magnitude of the velocity, this means that the object will have the same kinetic energy regardless of the direction of the velocity. Therefore, option C is correct.