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Cake day: June 28th, 2024

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  • We can safely ignore the acceleration time, so the distance is just terminal velocity times time. Catching up means equal distance for both, so

    v1*t1 = v2*t2
    

    Substituting t1 with t2+T, where T is the headstart, we can solve for t2:

    v1*(t2+T) = v2*t2
    v1*T = v2*t2-v1*t2
    t2 = (v1*T)/(v2-v1)
    

    v1*T is also the distance of the first jumper when the serving jumper jumps. So it’s headstart distance divided by the relative velocity.