Answer :
The speed of the pod and the space station after collision depends on
their initial momentum.
The speeds of the pod and space station are compared as follows;
- The change in the speed of the pod is [tex]-377.\overline{27}[/tex] times the change in speed of the base station and in the opposite direction.
Reasons:
The given information are;
Mass of the pod, m = 1100 kg
Mass of the space station, M = 415000 kg
Required:
To compare the speed of the pod and the base station after the collision
Solution:
Let v₁ represent the initial velocity of the Pod, let V₁ represent the initial
velocity of the space station, according to the conservation of linear
momentum principle, we have;
m·v₁ + M·V₁ = m·v₂ + M·V₂
Which gives;
1100·v₁ + 415000·V₁ = 1100·v₂ + 415000·V₂
[tex]v_2 = \dfrac{1100 \cdot v_1 + 415000 \cdot V_1 - 415000 \cdot V_2}{1100} = \dfrac{1100 \cdot v_1 + 415000 \cdot (V_1 - V_2)}{1100}[/tex]
[tex]v_2 = \dfrac{1100 \cdot v_1 + 415000 \cdot (V_1 - V_2)}{1100} = v_1 + \dfrac{4150}{11} \cdot (V_1 - V_2)[/tex]
Which gives;
[tex]\dfrac{v_2 - v_1 }{V_1 - V_2} = \dfrac{\Delta v}{-\Delta V} = \dfrac{4150}{11}[/tex]
[tex]\dfrac{\Delta v}{\Delta V} = -\dfrac{4150}{11} = -377\frac{3}{11} = -377.\overline{27}[/tex]
Where;
Δv = The change in the speed of the pod
ΔV = The change in the speed of the space station
The negative sign indicates a reversal in the direction of the speed
Therefore;
- The change in the speed of the pod is [tex]-377.\overline{27}[/tex] times the change in speed of the base station and in the opposite direction.
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