Astronomers estimate that a 2.0 km--wide asteroid collides with the Earth once e

Question

Astronomers estimate that a 2.0 km--wide asteroid collides with the Earth once every million years. The collision could pose a threat to life on Earth.

(Part A)
Assume a spherical asteroid has a mass of 3100 kg for each cubic meter of volume and moves toward the Earth at 16 km/s . How much destructive energy could be released when it embeds itself in the Earth?

E(ast) = ______ J


(Part B)
For comparison, a nuclear bomb could release about 4.0×10 to the 16 . How many such bombs would have to explode simultaneously to release the destructive energy of the asteroid collision with the Earth?

n= ____ bombs

Explanation / Answer

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! please dont forget to rate my answer :)

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