Question

Bullet 2 has twice the mass of bullet 1. Both are fired so that they have the same speed. If the kinetic energy of bullet 1 is , is the kinetic energy of bullet 2 (a) 0.25K, (b) 0.5K, (c) 0.71K, (d) K, or (e) 2K?

Short answer

The correct option is (e) 2K.

Step-by-step solution

Given information

The mass of bullet 1 is m.

The mass of bullet 2 is 2m.

The speed of both bullets is v.

The kinetic energy of bullet 1 is K.

Kinetic energy

For a body having a certain mass and traveling with a certain speed, the relation for the kinetic energy is given below:

$\mathrm{Kinetic}\mathrm{Energy}=\frac{1}{2}\left(\mathrm{Mass}\right)\times {\left(\mathrm{Speed}\right)}^2$

The kinetic energy of a moving body always relies on two factors, ‘body’s mass’ and ‘body’s speed,’ respectively.

Kinetic energy of bullet 2

The formula for the kinetic energy of bullet 1 is given by the following:

$\mathrm{K}=\frac{1}{2}{\mathrm{mv}}^2$

The formula for the kinetic energy of bullet 2 is given by the following:

$\begin{array}{l}K\text{'}=\frac{1}{2}\left(2m\right)v^2\\ K\text{'}=2\times \frac{1}{2}m{v}^2\\ K\text{'}=2K\end{array}$

Hence, the kinetic energy of bullet 2 is 2K, and the correct option is (e) 2K.