At a time when mining asteroids has become feasible, astronauts have connected a line between their 3760-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, 490 m apart. How much time does it take for the ship and the asteroid to meet

wouldn't it depend on which direction the engine is fired?

To find the time it takes for the ship and the asteroid to meet, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.

First, we need to calculate the acceleration of the system. By applying the force on the asteroid (490 N) to Newton's second law, we can find the acceleration of the asteroid:

Force = mass × acceleration
490 N = 6100 kg × acceleration

Rearranging the equation to solve for acceleration, we have:

acceleration = Force / mass
acceleration = 490 N / 6100 kg

Now, we have the acceleration of the asteroid. However, since the ship and the asteroid are connected by a line and the ship exerts a force on the asteroid, they both will have the same acceleration. Therefore, the acceleration of the system is also equal to the acceleration of the ship.

Next, we need to calculate the resulting net force on the system. The net force is the force exerted by the ship minus the force of friction between the asteroid and its surroundings since it is not explicitly given in the question. For simplicity, assume there is no friction. In that case, the net force is simply the force exerted by the ship:

Net force = 490 N

Now, we can calculate the acceleration of the system using Newton's second law:

acceleration = Net force / total mass
acceleration = 490 N / (3760 kg + 6100 kg)

With the acceleration known, we can use the kinematic equation to find the time it takes for the ship and the asteroid to meet. The kinematic equation for motion with constant acceleration is:

distance = (initial velocity × time) + (0.5 × acceleration × time^2)

In this case, the initial velocity of both the ship and the asteroid is zero, as they start from rest. The distance between them is given as 490 m. Plugging in these values, we have:

490 m = 0 × t + (0.5 × acceleration × t^2)

Simplifying the equation, we get:

0.5 × acceleration × t^2 = 490 m
acceleration × t^2 = 980 m
t^2 = 980 m / acceleration

Finally, we can solve for t by taking the square root of both sides:

t = √(980 m / acceleration)

Substituting the value of acceleration calculated earlier, you can find the numerical value of t.