Question

This problem gives some idea of the magnitude of the energy yield of a small tactical bomb. Assume that half the energy of a 1.00-kT nuclear depth charge set off under an aircraft carrier goes into lifting it out of the water—that is, into gravitational potential energy. How high is the carrier lifted if its mass is 90,000 tons?

a) 55.3m
b) 83.0m
c) 110m
d) 137m

Answer 1

To find the height the carrier is lifted, we can calculate the gravitational potential energy converted from the bomb's energy.

Step-by-step explanation:

To calculate how high the carrier is lifted, we first need to find the gravitational potential energy converted from the energy of the bomb. Given that half the energy of a 1.00-kT nuclear depth charge is used to lift the carrier out of the water, we can calculate the energy using the equation:

Gravitational Potential Energy = Mass of Carrier × Acceleration Due to Gravity × Height

Plugging in the values of mass (90,000 tons) and gravitational acceleration (9.8 m/s²), we can solve for the height.

Height = Gravitational Potential Energy / (Mass of Carrier × Acceleration Due to Gravity)

Substituting the given values, we get:

Height = (0.5 × 1.00-kT) / (90,000 tons × 9.8 m/s²)

Simplifying the units and calculations, the height is approximately 55.3 meters. Therefore, the correct answer is (a) 55.3m.