At a time when mining asteroids has become feasible, astronauts have connected a line between their 3460-kg space tug and a 6430-kg asteroid. They pull on the asteroid with a force of 366 N. Initially the tug and the asteroid are at rest, 493 m apart. How much time does it take for the ship and the asteroid to meet?

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Physics

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21 September, 06:41

At a time when mining asteroids has become feasible, astronauts have connected a line between their 3460-kg space tug and a 6430-kg asteroid. They pull on the asteroid with a force of 366 N. Initially the tug and the asteroid are at rest, 493 m apart. How much time does it take for the ship and the asteroid to meet?

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Brooks Mclaughlin · Answer 1

77.8s

Explanation:

Let d distance between the asteroid and space tug

So; d=Xtug+Xspace

Xtug=VtT+0.5atT^2

Xspace=VsT+0.5asT^2

Since Vt=Vs=0 initial velocity

Then

d=0.5 (atT^2+asT^2)

T^2 (at+as) = 2d

T=√ (2d/at+as)

But force F = mass M*acceleration a

Hence at=Ft/mt, as=Fs/ms

But note Ft=F=Fs since the Same force acts on it

Hence T=√ (2d/F (1/mt+1/Ms))

T=√ (2*493/366 (1/3460+1/6430)

T=√ (986/0.1627) = √ (6060.195) = 77.8s