A 3.0×1010kg asteroid is heading directly toward the center of the earth at a st

Question

A 3.0×1010kg asteroid is heading directly toward the center of the earth at a steady 16 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 5.5×106km away from earth. You can ignore the rotational motion of the earth and asteroid around the sun.

Part A

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

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

Part B

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

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

Part C

The rocket fires at full thrust for 160 s before running out of fuel. Is the earth saved?

Explanation / Answer

A) given that the asteroid is moving at constant speed = 16 km /s = 16*3600 km / h

The distance it had to travel to reach earth surface

= 5.5*10^6 - 6400

Time taken = distance / speed

= 5.5*10^6 -6400 /16 *3600

= 95 hours

B) The minimum angle by which it should be deflected be p

Tan p = 6400 / 5.5*10^6

Angle p = 0.67 °

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.