Question

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?

Answer 1

The time it takes for the ship and the asteroid to meet is approximately 493 seconds.

Step-by-step explanation:

To determine the time it takes for the ship and the asteroid to meet, we can use the equations of motion. Since the initial velocities of both the tug and the asteroid are zero, we can use the equation d = v0t + (1/2)at2, where d is the initial distance between them, v0 is the initial velocity, a is the acceleration, and t is the time. Rearranging the equation to solve for t, we have t = sqrt(2d/a). Substituting the given values, we get t = sqrt(2 * 493 / (366 / (3460 + 6430))) = 493 s.

Answer 2

77.8s

Step-by-step 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