Question

Which has the larger kinetic energy, a 10 g bullet fired at500 m/s or a 75 kg student running at 5.5 m/s?

Answer 1

Given:

Mass of bullet = 10 g

Speed of bullet, v = 500 m/s

Mass of student = 75 kg

Speed of student, v = 5.5 m/s

Let's find which has the larger kinetic energy.

To find the kinetic energy of each, apply the formula:

$KE=\frac{1}{2}mv^2$

Where:

m is the mass in kg

v is the speed in m/s

KE is the kinetic energy.

• Kinetic energy for bullet:

Where:

m = 10 g = 0.01 kg

v = 500 m/s

$KE_{bullet}=\frac{1}{2}*0.01*500^2=1250\text{ J}$

The kinetic energy of the bullet is 1250 J.

• Kinetic energy for the student:

Where:

m = 75 kg

v = 5.5 m/s

$KE_{boy}=\frac{1}{2}*75*5.5^2=1134.38\text{ J}$

The kinetic energy of the boy is 1134.38 J.

Thus, we have:

Kinetic energy of the bullet > Kinetic energy of the student

Therefore, the bullet has the larger kinetic energy.