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A spaceship, at rest in an inertial frame in space, suddenly needs to accelerate. The ship forcibly expels 103 kg of fuel from its rocket engine, almost instantaneously, at velocity [tex](\frac{3}{8})c[/tex] in the original inertial frame. Afterwards, the ship has a mass of 106 kg. How fast will the ship then be moving, valid to three significant figures?

Answer :

Answer:

[tex]V_s = 1.8*10^5m/s[/tex]

Explanation:

There is no external force applied, therefore there is a moment's preservation throughout the trajectory.

Initial momentum = Final momentum.

The total mass is equal to

[tex]m_T= m_1 +m_2[/tex]

Where,

[tex]m_1 =[/tex] mass of ship

[tex]m_2 =[/tex] mass of fuell expeled.

As the moment is conserved we have,

[tex]0=V_fm_2+V_sm_1[/tex]

Where,

[tex]V_f =[/tex] Velocity of fuel

[tex]V_s =[/tex]Velocity of Space Ship

Solving and re-arrange to [tex]V_s[/tex]we have,

[tex]V_s = \frac{V_f m_2 }{m_1}[/tex]

[tex]V_s = \frac{3/5c}{10^6}[/tex]

[tex]V_s = 3.5*10^{-3}c[/tex]

Where c is the speed of light.

Therefore the ship be moving with speed

[tex]V_s = \frac{3}{5}*10^{-3}*3*10^8m/s[/tex]

[tex]V_s = 1.8*10^5m/s[/tex]

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