At a time when mining asteroids has become feasible, astronauts have connected a line between their 3740-kg space tug and a 6500-kg asteroid. They pull on the asteroid with a force of 470 N. Initially the tug and the asteroid are at rest, 480 m apart. How much time does it take for the ship and the asteroid to meet?
each are being pulled by a force of 470N.
the acceleraration of each is 470/masseach
so relative acceleration is the sum..
arelative=470/3740+470/6500
add those.
d=1/2 a t^2 where d is 480m, and a is relative acceleration.
To determine the time it takes for the ship and the asteroid to meet, we can use Newton's second law of motion.
Newton's second law states that the net force acting on an object is equal to its mass multiplied by its acceleration:
F = m * a
In this scenario, the net force acting on the asteroid is the force applied by the tug, which is 470 N. The mass of the asteroid is 6500 kg. We can rearrange the equation to solve for acceleration:
a = F / m
a = 470 N / 6500 kg
a ≈ 0.0723 m/s²
Now that we know the acceleration of the asteroid, we can use the formula of motion to calculate the time it takes for the ship and the asteroid to meet. The formula of motion is:
s = ut + (1/2) * a * t²
where s is the displacement, u is the initial velocity, a is acceleration, and t is time. In this case, the initial velocity is 0 m/s because the asteroid and the ship are at rest initially. The displacement (s) is 480 m.
480 = 0 * t + (1/2) * 0.0723 * t²
We can solve this equation for t. Simplifying the equation, we get:
0.03615 * t² = 480
t² = 480 / 0.03615
t² ≈ 13278.7425
t ≈ √13278.7425
t ≈ 115.28 seconds (rounded to two decimal places)
Therefore, it takes approximately 115.28 seconds for the ship and the asteroid to meet.