Question

in the navy, the ships speed is typically referred to in knots. if one knot is equal to approximately 1.15 miles per hour, 25 knots equals approximately 28.8 mph and 100 knots equals about 115 mph. determine the kinetic energy in joules of a 90,000-metric ton aircraft carrier travelling at 30 knots.

Answer 1

The kinetic energy of the 90,000-metric ton aircraft carrier traveling at 30 knots is approximately 10,710,956,800 joules.

To determine the kinetic energy of the aircraft carrier, we need to use the formula:

Kinetic energy = (1/2) * mass *
`velocity^2`

First, we need to convert the speed from knots to meters per second (m/s) since the kinetic energy formula requires the velocity in meters per second.

Given that 1 knot is approximately equal to 0.5144 meters per second (m/s), we can calculate the velocity in m/s.

30 knots * 0.5144 m/s = 15.432 m/s (approximately)

Next, we need to convert the mass of the aircraft carrier from metric tons to kilograms since the kinetic energy formula requires the mass in kilograms.

Given that 1 metric ton is equal to 1000 kilograms, we can calculate the mass in kilograms.

90,000 metric tons * 1000 kg/metric ton = 90,000,000 kg

Now that we have the velocity and the mass in the correct units, we can calculate the kinetic energy.

Kinetic energy = (1/2) * mass *
`velocity^2`

= (1/2) * 90,000,000 kg *
`(15.432 m/s)^2`

= 1/2 * 90,000,000 kg * 238.024224
`m^2/s^2`

= 10,710,956,800 joules

Therefore, the kinetic energy of the 90,000-metric ton aircraft carrier traveling at 30 knots is approximately 10,710,956,800 joules.