As the spaceship pull the asteroid with 620 N of force, they will meet after 105.4 seconds.
The gravitational force between the ship and the asteroid is very small compared to the force caused by pulling the asteroid. Hence, we can assume that the only force applied on the asteroid is the pulling force.
Using the Newton 2nd Law of motion:
F = m . a
Where
F = pulling force = 620 N
m = mass of the asteroid = 7700 kg
a = acceleration
Hence,
a = F/ m = 620 / 7700 = 0.081 m/s²
Using the equation of motion:
s = 1/2 . a t²
Where:
s = distance = 450 meters
t = time
Hence,
450 = 1/2 . (0.081) t²
t² = 11,111.11
t = 105.4 seconds
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