Astronomers estimate that a 2
-
km wide asteroid collides 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
. How many such bombs would have to
explode simultaneously to release the
destructive energy of the asteroid collision with Earth?

Question

Astronomers estimate that a 2
-
km wide asteroid collides 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 
. How many such bombs would have to 
explode simultaneously to release the 
destructive energy of the asteroid collision with Earth?

anonymous · Answer

so we are given that the astroid is spherical and has a width (aka diameter) of 2km wide.
we will break the question up into steps.

first, find the volume of the astroid, using the equaiton of a sphere 
$$\frac{ 4 }{ 3 }\times \pi \times r ^{3} = volume$$
where r is the radius of the sphere