NASA has taken an increased interest in near Earth asteroids. These objects, popularized in recent blockbuster movies, can pass very close to Earth on a cosmic scale, sometimes as close as 1 million miles. Most are small—less than 500 m across—and while an impact with one of the smaller ones could be dangerous, experts believe that it may not be catastrophic to the human race. One possible defense system against near Earth asteroids involves hitting an incoming asteroid with a rocket to divert its course. Assume a relatively small asteroid with a mass of 2.10∙1010 kg is traveling toward the Earth at a modest speed of 12.0 km/s.
a) How fast would a large rocket with a mass of 8.00∙104 kg have to be moving when it hit the asteroid head on in order to stop the asteroid?
b) An alternative approach would be to divert the asteroid from its path by a small amount to cause it to miss Earth. How fast would the rocket of part (a) have to be traveling at impact to divert the asteroid's path by 1.00°? In this case, assume that the rocket hits the asteroid while traveling along a line perpendicular to the asteroid s path.
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