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Answer :
To find the final velocity of a space probe after it ejects part of its mass, the conservation of momentum principle is applied. By using the initial masses and velocities along with the mass and velocity of the ejected exhaust, one can calculate the probe's final velocity.
The question you've asked pertains to the principle of conservation of momentum in physics, specifically when a space probe fires its engines in space. To find the final velocity of the probe after it ejects some of its mass, we use the formula derived from the conservation of momentum, which states that the total momentum of a system before an event is equal to the total momentum of the system after the event.
Let's denote:
- m as the mass of the probe before ejecting exhaust,
- m_e as the mass of the ejecting exhaust,
- u as the initial velocity of the probe relative to the Sun,
- v_e as the velocity of the ejected exhaust relative to the probe,
- v_f as the final velocity of the probe after ejecting exhaust.
Applying the principle of conservation of momentum:
m*u = (m - m_e)*v_f + m_e*(v_f - v_e)
Plugging in the given values: 6780 kg for m, 65 kg for m_e, 126 m/s for u, and 223 m/s for v_e (but remember, v_e is relative to the space probe, so it is in the opposite direction, hence negative when considering the system's overall momentum), we can solve for v_f. This calculation yields the final velocity of the space probe after the exhaust is ejected.
The final velocity of the space probe is found by rearranging the equation for v_f and solving.
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Answer: The final velocity of the probe is 128.15 m/s
Explanation: Please see the attachments below
