Question

At a time when mining asteroids has become feasible, astronauts have connected a line between their 3220-kg space tug and a 6240-kg asteroid. They pull on the asteroid with a force of 362 N. Initially the tug and the asteroid are at rest, 311 m apart. How much time does it take for the ship and the asteroid to meet

Answer 1

-- F = m a ... ==>  a = F/m

-- The tension in the rope is 362 N.  That same force acts on the asteroid and on the tug, pulling them together.

-- The asteroid's acceleration is 362N / 6240 kg = 0.058 m/s², headed for a point on the rope somewhere between the asteroid and the tug.

-- The tug's acceleration is 362 N / 3220 kg = 0.112 m/s², also headed for a point on the rope somewhere between the tug and the asteroid.

-- So now we have a gap between them, initially 311 m long, closing with a speed that starts at zero and accelerates at  0.170 m/s² .

-- D = (1/2) a T²

311 m = (1/2) (0.170 m/s²) (T²)

T²  =  311 m / 0.085 m/s²

T = √(311/0.085)  seconds

T = 60.41 seconds

The answer I get is so durn near 60 seconds (1 minute) that it suggests two things to me:  ==> That's where the weird numbers of 362N and 311m came from, and ==> there's a good chance that my answer is correct.

Note:  It's important to me that you know that 5 points for this one is really cheap and chintzy, and the reason I decided to try it was only to see whether I could.