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Question

At a time when mining asteroids has become feasible, astronauts have connected a line between their 3040-kg space tug and a 5720-kg asteroid. They pull on the asteroid with a force of 341 N. Initially the tug and the asteroid are at rest, 312 m apart. How much time does it take for the ship and the asteroid to meet?

Answer 1

The force acts on both objects and accelerates them towards each other.  The entire system has a mass of 3040 + 5720 kg = 8760 kg.

 

Since F = ma, a = F/m.  So A force of 341 N results in an acceleration of 341 / 8760 m / sec² = 0.0389 m / sec².

 

Since they are at rest with each other initially, the distance between them decreases at 1/2 at².

 

So in order for the distance to go to 0, 1/2 at² has to equal their starting distance of 312 m.

 

1/2 * 0.0389 m / sec² * t² = 312

 

t² = 2 * 312 / 0.0389 = 16041.1 sec²

 

t = 126.65 seconds