# The amount of kinetic energy an object has, depends on its mass and its speed. Rank the following...

## Question:

The amount of kinetic energy an object has, depends on its mass and its speed. Rank the following sets, of oranges and cantaloupes, from least kinetic energy, to greatest kinetic energy. If two sets have the same amount of kinetic energy, place one on top of the other.

## Kinetic Energy:

Let us assume a dark donkey of mass (m) is running on the road with a constant speed (v). In this scenario, the kinetic energy of the dark donkey can be expressed as,

{eq}K = \frac{1}{2}mv^{2}. {/eq}

The energy (kinetic) of a moving object is expressed in Joules (J).

In the given problem, the information about the masses and the speeds of the oranges and cantaloupes are not provided.

Suppose the details are as below:

Orange 1:

Mass (m) = 1 kg

Speed (v) = 2 m/s

Orange 2:

Mass (m) = 0.5 kg

Speed (v) = 1.5 m/s

Cantaloupe 1:

Mass (m) = 1.5 kg

Speed (v) = 1.0 m/s

Cantaloupe 2:

Mass (m) = 2.5 kg

Speed (v) = 0.5 m/s

Thus, the kineti energies of these fruites can be expressed as,

{eq}\begin{align*} K_{1} &= \frac{1}{2}mv^{2}\\ K_{1} &= \frac{1}{2} \times 1 \times (2)^{2}\\ K_{1} &= 2.0 \ \rm J.\\ \end{align*} {/eq}

{eq}\begin{align*} K_{2} &= \frac{1}{2}mv^{2}\\ K_{2} &= \frac{1}{2} \times 0.5 \times (1.5)^{2}\\ K_{2} &= 0.56 \ \rm J.\\ \end{align*} {/eq}

{eq}\begin{align*} K_{3} &= \frac{1}{2}mv^{2}\\ K_{3} &= \frac{1}{2} \times 1.5 \times (1.0)^{2}\\ K_{3} &= 0.75 \ \rm J.\\ \end{align*} {/eq}

{eq}\begin{align*} K_{4} &= \frac{1}{2}mv^{2}\\ K_{4} &= \frac{1}{2} \times 2.5 \times (0.5)^{2}\\ K_{4} &= 0.31 \ \rm J.\\ \end{align*} {/eq}

Thus, the kinetic energies in the increasing order can be given as,

{eq}\boxed{K_{4} < K_{2} < K_{3} < K_{1}}. {/eq}