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.

a) Assume a spherical asteroid has a mass of 3500 kg for each cubic meter of volume and moves toward the Earth at 14 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 simultaneously to release the destructive energy of the asteroid collision with the Earth?

Answer 1

a)

volume of asteroid,

V = (4/3) * pi * r³

where r is radius, r = 1 km = 1000 m

so,

V = (4/3) * pi * 1000³

V = 4.188e9 m³

so,

mass is given as

m = 3500 kg / m³ * 4.188e9 m³

m = 1.466e13 Kg

so,

K.E = 1/2mv²

K.E = 1/2 * 1.466e13 * 14000²

K.E = 1.4367e21 J

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(b)

number of bombs

N = 1.4367e21 / 4.0×10¹⁶

N = 35918 bombs