Question

Astronomersestimatethata2.0-km-diameterasteroidcollides with the Earth once every million years. The collision could pose a threat to life on Earth. (a) Assume a spherical asteroid has a mass of 3200 kg for each cubic meter of volume and moves toward the Earth at 15 km????s. How much destructive energy could be released when it embeds itself in the Earth? (b) For comparison, a nuclear bomb could release about 4.0 * 1016 J. How many such bombs would have to explode

Answer 1

Step-by-step explanation:

Below is an attachment containing the solution.

Answer 2

a) 1.6*10^21 Joules.

b) 40,000

Step-by-step explanation:

part a )

maximum destructive energy that can be released is the case when all the kinetic energy of the asteroid is consumed.

therefore E = 1/2 m v^2

m= density * volume

= 3100* (4/3* pi * 1000^3 ) = 12978666666666.67 kg

given v = 16000m/s

therefore

E= 1/2 * 12978666666666.67 * 16000 * 16000

= 1.6 x 10^21 Joules!

part B)

each bomb is capable of 4 x 10^16 joules

therefore no of bombs that are needed to produce the required energy are

1.6 x 10^21 / 4 x 10^16 = 40,000

that is 40,000 such nuclear bombs are required!