A 4.0 × 10¹⁰ kg asteroid is heading directly toward the center of the earth at a steady 20 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 × 10⁹ N of thrust. The rocket is fired when the asteroid is 4.0 × 10⁶ km away from earth. You can ignore the earth’s gravitational force on the asteroid and their rotation about 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?
c. What is the actual angle of deflection if the rocket fires at full thrust for 300 s before running out of fuel?