One of the greatest mass extinctions occurred about 65 million years ago, when,

Question

One of the greatest mass extinctions occurred about 65 million years ago, when, along with many other life-forms, the dinosaurs went extinct. Most geologists and paleontologists agree that this event was caused when a large asteroid hit the earth. Scientists estimate that this asteroid was about 10 km in diameter and that it would have been traveling at least as fast as 11 km/s. The density of asteroid material is about 3.5 g/cm3, on the average. It has been suggested that we can protect the earth from such devastating asteroidal impacts by using nuclear devices to alter the orbits of such asteroids around the sun so that they will miss our planet. If this is done very far from earth, it is necessary to move them only a few centimeters to spare the earth a mass extinction. How much energy would it take to move the asteroid that has been implicated in the dinosaur extinction by a few centimeters? To make the calculation reasonable, assume that we need to exert a force on the asteroid that will accelerate it uniformly from rest through a distance of 5.00 cmin 0.500 s . The energy we must give to the asteroid is the added kinetic energy from this motion. One ton of TNT releases 4.18×109 J .

To see if it is feasible to do this, how many 1 megaton bombs would it take to accomplish the task? please help...

Explanation / Answer

d = 5 cm = 0.05 m
t=0.5 s
use:
d = vi*t + 0.5*a*t^2
0.05 = 0 + 0.5*a*(0.5)^2
a=0.4 m/s^2

now sue:
vf = vi+a*t
= 0 + 0.4*0.5
= 0.2 m/s

So asterroid should have velocity of 0.2 m/s
Volume = (4/3)*pi*r^3
= (4/3)*pi*(5*10^3 m)^3
=5.236*10^11 m^3

density = 3.5 g/cm^3 = (3.5*10^-3 Kg) / (10^-6 m^3) = 3.5*10^3 Kg/m^3

mass = density * volume = 3.5*10^3*5.236*10^11 = 1.833*10^15 Kg

Energy required = kinetic energy = 0.5*m*vf^2
= 0.5* 1.833*10^15 *(0.2)^2
=3.7*10^13 J

This much amount of energy must be supplied by nuclear weapon

1 mega ton = 10^6 ton
energy released by 1 megaton = 10^6*4.18*10^9 = 4.18*10^15 J

Number of bombs = 3.7*10^13 /4.18*10^15   
1 bomb is enough

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