Afederation 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.

The starship moves by 16.5 m (nearest tenth)

Molybdeum(mo)orruthenium (ru)actually, elements with similar chemical properties as technetium would bemn, re, and bh. this is because elements in the same group/family (column) have similar chemical properties. elements in the same period (row) have the same number of energy levels (or shells).

Newton's first law describes something special that results from the sum of all the external forces (including gravity) on an object.