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How can you use this information about mass to help you compare the speed of the pod after the collision to the speed of the space station after the collision?
Pod: 1100KG Space station: 415000kg


Sagot :

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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