I am trying to do the following vector integral. When the force and the initial motion are along the same line it is easy but when they are not I can't do the integration. Hints would be appreciated.(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \vec F = \frac {d} {dt} \vec p [/tex] where [tex] \vec F = (0, F_{y},0) [/tex] and [tex] \vec {p} [/tex] can be written as [tex] \vec p = m_{o} \vec u / \sqrt {1 - u^{2}/c^{2} }[/tex]

At time t = 0, [tex] \vec u = (0,u_{o},0) [/tex]

When I replace p with its equivalent in u I get into trouble because [tex]u^{2} = \vec u \cdot \vec u [/tex] and so both integrals involve both x & y components.

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# Integration involving a dot product

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