- #1
Ohoneo
- 22
- 0
Homework Statement
At a time when mining asteroids has become feasible, astronauts have connected a line between their 3700-kg space tug and a 6100-kg asteroid. Using their ship's engine, they pull on the asteroid with a force of 490 N. Initially the tug and the asteroid are at rest, 460 m apart. How much time does it take for the ship and the asteroid to meet?
Homework Equations
F = ma
x = x0+ v0t + 1/2 a t2
v = v a t
v2-v02 = 2a (x - x0)
The Attempt at a Solution
I tried to solve this a couple of ways and got it wrong both times.
First, I found the acceleration of the asteroid by doing F = ma, and dividing 490 by 6100 kg. I got .0803 (approximately, I didn't round in my work, but I'll round for ease of typing) m/s2.
I then tried two equations, which both gave me the same answer:
First, I plugged into v2-v02 = 2a (x-x0)
and got v = 8.5966 for the final velocity of the asteroid.
I then plugged into v = v a t to find how long it would take to get to that velocity. I got t = 107 seconds.
When I got the answer wrong, I tried again by plugging into x = x0+ v0t + 1/2 a t2
I plugged in: 460 = 0 + 0 + 1/2 (.803)t2
and I got t = 107 seconds again.
Any help would be much appreciated :)