Question

CHALLENGE A comet with a mass of

7.85 x10" kg strikes Earth at a speed of
25.0 km/s. Find the kinetic energy of the comet in joules, and compare the work that is done by Earth in stopping the comet to the 4.2×1015 J of energy that was released by the largest nuclear weapon ever exploded

Answer 1

The kinetic energy of the comet is 2.46 x 10^15 J. The work done by Earth in stopping the comet is about 58.6% of the energy released by the largest nuclear weapon.

Step-by-step explanation:

The kinetic energy of an object is given by the formula KE = 1/2 * m * v^2, where m is the mass and v is the velocity of the object. In this case, the mass of the comet is 7.85 x 10^9 kg and its velocity is 25.0 km/s. To find the kinetic energy, we can substitute these values into the formula:

KE = 1/2 * (7.85 x 10^9 kg) * (25.0 km/s)^2

Using the given value of 1 km = 1000 m, we can convert the velocity to m/s: (25.0 km/s) * (1000 m/km) = 25000 m/s

Substituting this value and the mass into the formula:

KE = 1/2 * (7.85 x 10^9 kg) * (25000 m/s)^2

= 2.46 x 10^15 J

The kinetic energy of the comet is 2.46 x 10^15 J.

To compare this energy to the 4.2 x 10^15 J released by the largest nuclear weapon, we can simply calculate the ratio:

Ratio = (2.46 x 10^15 J) / (4.2 x 10^15 J)

= 0.586

The work done by Earth in stopping the comet is about 58.6% of the energy released by the largest nuclear weapon.