Question

A horse and a dog are running with the same speed. What is the ratio of their kinetic energies if the weight of horse is $10$ times that of the dog?

Answer 1

Step 1: Given data and assumptions

Let the speed of the horse be, $v$

Therefore, the speed of the dog will also be $v$

Let the mass of the dog be $m$

Therefore the mass of the horse will be, $10\times m=10m$

Step 2: Calculating the ratio of kinetic energies

Kinetic energy is given as,

$KE=\frac{1}{2}m{v}^2$

where, $m$ is mass and $v$ is velocity.

Let the kinetic energy of the horse be $K{E}_1$ and the kinetic energy of the dog be $K{E}_2$.

Therefore, the ratio of their kinetic energies will be,

$$\begin{gathered} \frac{K{E}_1}{K{E}_2}=\frac{1/2\times 10m\times v^2}{1/2\times m\times v^2} \\ \frac{K{E}_1}{K{E}_2}=\frac{10}{1} \end{gathered}$$

Therefore, the ratio of the kinetic energies is, $10:1$.