Calculating the Velocity Needed to Match the Kinetic Energy of a Bullet

Question:

How fast would an 82 kg man need to run in order to have the same kinetic energy as an 8.0 g bullet fired at 420 m/s? Express your answer with the appropriate units.

Answer:

4.14846 m/s

Explanation:

The equation used to calculate the kinetic energy of an object is:

KE = (1/2) * mass * (velocity)^2

So, first we need to find the kinetic energy of the bullet:

KE_Bullet = (1/2) * .008 kg * (420 m/s)^2

KE_Bullet = 705.6 J

Now, since we want the man running to have the same energy, we use the kinetic energy of the bullet in our calculation:

705.6 J = (1/2) * (82 kg) * (V_man m/s)^2

V_man = √((705.6 J * 2) / 82 kg)

V_man = 4.14846 m/s

Therefore, the velocity an 82 kg man would need to reach in order to have the same kinetic energy as an 8 g bullet fired at 420 m/s is 4.14846 m/s.

Cheers!