A Federation starship (8.5 ✕ 106 kg) uses its tractor beam to pull a shuttlecraft (1.0 ✕ 104 kg) aboard from a distance of 14 km away. The tractor beam exerts a constant force of 4.0 ✕104 N on the shuttlecraft. Both spacecraft are initially at rest. How far does the starship move as it pulls the shuttlecraft aboard?

Refer to the diagram shown below.

m₁ = 8.5 x 10⁶ kg, the mass of the starship

m₂ = 10⁴ kg, the mass of the shuttlecraft

a₁ = the acceleration of the starship

a₂ = the acceleration of the shuttle

F = 4 x 10⁴ N, the pulling force

Let y = distance traveled by the starship

Let x = distance traveled by the shuttlecraft

If t = the time of travel, then

y = 0.5a₁t² (1)

x = 0.5a₂t² (2)

F = m₁a₁ = m₂a₂ (3)

Also,

x + y = 14000 m (4)

From (2), obtain

a₁ = (4 x 10⁴ N) / (8.5 x 10⁶ kg) = 4.706 x 10⁻³ m/s²

a₂ = (4 x 10⁴ N) / (10⁴ kg) = 4 m/s²

From (1), (2) and (4), obtain

0.5 * (t s) ² * (4 + 4.706 x 10⁻³ m/s²) = 14000 m

2.002353t² = 14000

t² = 6991.774 s²

t = 83.617 s

Therefore

x = 0.5*4*6991.774 = 13984 m = 13.984 km

y = 0.5*4.706 x 10⁻³*6991.774 = 16.452 m

The starship moves only about 16.5 m while pulling in the shuttlecraft by 13.98 km.

Answer: The starship moves by 16.5 m (nearest tenth)