At a time when mining asteroids has become feasible, astronauts have connected a line between their 3180-kg space tug and a 5810-kg asteroid. They pull on the asteroid with a force of 574 N. Initially the tug and the asteroid are at rest, 540 m apart. How much time does it take for the ship and the asteroid to meet?

Question

anonymous · Answer

Well if the tug keeps on pulling, they will never meet.

mrnood · Answer

@alanevans This assumes that the ship has another force acting upon it, such that it continues to accelerate, towing the asteroid behind it.

Since the 2 bodies are initially at rest, and no other force is mentioned then I would interpret it as the situation where the 'tug' is winching the asteroid towards it with a line in constant tension.

In this case they will accelerate towards each other, until they collide, wiping out the tug and all within it.

But it would still be interesting to know how long it would take!

Since the line is in constant tension I would take each body as having an acceleration given by F=ma

You have F and m for each body - so calculate a

Since the tension acts opposite then then they will accelerate towards each other. From the perspective of 1 body, the other will be seen to accelerate towards it with the sum of the 2 accelerations calculated above.

You now have s= ut +0.5at^2

where u = 0, so solve for t