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!