What Is the Velocity of a Probe Released from a Moving Spaceship?

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SUMMARY

The problem involves a spaceship moving at a velocity of 0.75c in the x-direction, which releases a probe moving at 0.75c in the y-direction relative to the spaceship. To find the probe's velocity as observed from Earth, the velocity-addition formula must be applied, specifically for orthogonal velocities. The solution requires understanding the effects of time dilation and the use of 4-vectors to accurately calculate the resultant velocity in both magnitude and direction.

PREREQUISITES
  • Understanding of special relativity concepts, particularly velocity addition.
  • Familiarity with the velocity-addition formula for orthogonal velocities.
  • Knowledge of time dilation effects in relativistic physics.
  • Basic understanding of 4-vectors and their application in physics.
NEXT STEPS
  • Study the velocity-addition formula in special relativity, focusing on orthogonal components.
  • Learn about time dilation and its implications in relativistic scenarios.
  • Explore the concept of 4-vectors and their role in relativistic physics.
  • Review examples of similar problems involving velocities in different directions to solidify understanding.
USEFUL FOR

Students of physics, particularly those studying special relativity, and educators looking for examples of velocity addition in relativistic contexts.

jturko
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Homework Statement


A spaceship moves with a velocity 0.75c xhat with respect to the earth. The ship releases a probe with a velocity 0.75c yhat relative to the ship. What is the velocity of the probe as viewed on earth, magnitude and direction?

Homework Equations


The velocity-addition formulae for all three spatial directions

The Attempt at a Solution


I think that the velocity observed in the x direction of the probe will just be 0.75c, but I am having trouble wrapping my head around finding the velocity in the other directions. I know the velocity is changed due to the time dilation but cannot find the necessary equations to use. I think we are supposed to use 4-vectors
 
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