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Physics

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  • $\begingroup$ Since you stipulate that the velocity of the boat in the water's frame ($\vec v_b$) is constant, nothing else matters. The velocity is $\vec v =\vec v_b + \vec v_{current}$ in all frames, assuming $v_i \ll c$, so the answer is $\vec P + \vec vt$. $\endgroup$
    – JEB
    Commented Apr 4 at 18:11
  • $\begingroup$ @JEB what are v_i and c? $\endgroup$
    – Majid
    Commented Apr 4 at 18:32
  • $\begingroup$ the former is an abstract subscript standing for all velocity subscripts, and $c=1$ is, as aways, the speed of light. $\endgroup$
    – JEB
    Commented Apr 6 at 15:05