(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

2) If a relativistic rocket has a proper acceleration alpha that

increases with proper time tau according to:

alpha(tau) = 2/[Cosine(tau)^2 - Sine(tau)^2]

find its motion, r(t), from the point of view of a control tower

for whom the rocket is motionless at r(0) = 0.

(Hint: alpha(tau) here is the derivative with respect to tau of

ln[tan(tau + pi/4)] .)

2. Relevant equations

1. R=Rapidity

2. tanh(R)=β

3. d/dτ(R)=α

3. The attempt at a solution

Using formula #3 and the hint, I have R. Using formula #2 and my TI-89, I got:

(1-β)/2 = cos[t*(sqrt(1-β^2)+pi/4]^2

Using a couple of trig formulas, I have

β-1 = sin(2*t*sqrt(1-β^2))

I'm stuck there. As far as I know, there is no way to solve for β, and thus for the velocity 'v', which means I can't integrate to find r(t).

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Astrophysics - Special Relativity

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