Question

Work-Energy Theorem and conservation of Energy: A bullet that has a mass of 100 g is fired straight up from a gun with a velocity of 2000

ft/s​ from the top of a 150 m cliff. a. What is the kinetic energy of the bullet just after it was fired? b. What is the total potential energy of the bullet just before it was fired?

Answer 1

• a. The kinetic energy of the bullet just after it was fired is approximately 18,600 J.
• b. The total potential energy of the bullet just before it was fired is 147 J.

Step-by-step explanation:

a. To find the kinetic energy of the bullet just after it was fired, we can use the formula for kinetic energy:

Kinetic energy (KE) = 1/2 * mass * velocity²

Given:

• Mass of the bullet = 100 g = 0.1 kg
• Velocity of the bullet just after being fired = 2000 ft/s

Converting the velocity from ft/s to m/s:

• 1 ft = 0.3048 m
• 1 s = 1 s

Velocity in m/s = 2000 ft/s * 0.3048 m/ft * 1 s/1 s = 609.6 m/s

Substituting the values into the formula for kinetic energy:

KE = 1/2 * 0.1 kg * (609.6 m/s)²

Calculating this expression gives us:

KE ≈ 18,600 J

Therefore, the kinetic energy of the bullet just after it was fired is approximately 18,600 J.

b. To find the total potential energy of the bullet just before it was fired, we need to consider both gravitational potential energy and potential energy due to the height of the cliff.

Gravitational potential energy (PEg) is given by the formula:

PEg = mass * gravitational acceleration * height

Given:

• Mass of the bullet = 100 g = 0.1 kg
• Gravitational acceleration = 9.8 m/s²

Substituting the values into the formula for gravitational potential energy:

PEg = 0.1 kg * 9.8 m/s² * 150 m

Calculating this expression gives us:

PEg = 147 J

The potential energy due to the height of the cliff is equal to the gravitational potential energy, so the total potential energy of the bullet just before it was fired is also 147 J.

Therefore, the total potential energy of the bullet just before it was fired is 147 J.