A 3.9×10^10kg asteroid is heading directly toward the center of the earth at a s

Question

A 3.9×10^10kg asteroid is heading directly toward the center of the earth at a steady 21 km/s . To save the planet, astronauts strap a giant rocket to the asteroid perpendicular to its direction of travel. The rocket generates 5.0×10^9N of thrust. The rocket is fired when the asteroid is 5.0×10^6kmaway from earth. You can ignore the rotational motion of the earth and asteroid around the sun.

a) If the mission fails, how many hours is it until the asteroid impacts the earth?

b)The radius of the earth is 6400 km. By what minimum angle must the asteroid be deflected to just miss the earth?

Explanation / Answer

a)
t = d/v = (5.0*10^9 m)/(21*10^3m/sec)
t = 2.4*10^5 sec = 66.67 hrs = 2 days 18 hrs 40 min

(b)
tanq= 6400 km/(5.0*10^6 km)
tanq= 0.00128
q = tan^-1(0.00128)
q = 0.073 deg

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