Question

A 3.9×10¹⁰kg asteroid is heading directly toward the center of the earth at a steady 22 km/s. To save the planet, astronauts strap a giant rocket to the asteroid perpendicular to its direction of travel. The rocket generates 5.0×10⁹N of thrust. The rocket is fired when the asteroid is 3.8×10⁶km away from earth. You can ignore the rotational motion of the earth and asteroid around the sun.

Express your answers to two significant figures and include the appropriate units.

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) The rocket fires at full thrust for 430 ss before running out of fuel. Is the earth saved?

Answer 1