Contest Information

This is the current Steam Marines contest where the top 3 winners can earn Steam Marines keys redeemable via Humble! Rules for this contest:

  • Must email your answer, with work, to yjseow@worthlessbums.com.
  • Your work must be correct or close enough that I feel you've suffered enough.
  • Limit two attempts per person per contest.
  • Deadline is enforced based on when I receive the email.
  • Winners are choosen based on speed, correctness, and general awesomeness.

      • Current Contest

      A steampunk spaceship is initially at rest in frame of reference R. A navigational officer is startled by an alarm clock and accidentally jump starts the ship's engines. The ship starts to accelerate with constant proper acceleration A.

      If steampunk spaceships travel slower than the speed of light, what is the relative speed of the spaceship when the alarm clock reads time T?

      (Contest ends 27 October 2013.)

      Contest is over! Solution below:
      1) Start with the velocity addition formula.

      v = v1 + v2
      1 + v1v2/c2
      2) By the definition of proper acceleration we have v1 = v(t) and v2 = a dt. Substitute and expand in terms of dt:
      dv/dt = a - av2
      c2
      3) Integrating using 1/(1-z2) = 1/2(1-z)+1/2(1+z) gives:
      ln ((1+v/c)/(1-v/c)) = 2at/c

      4) Exponate and solve for v:
      v(t) = ctanh(at/c)

      5) You don't need me to explain how to get speed from velocity, right? :)