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touqra
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I have another difficult question regarding calculus of variations.
A particle travels in the (x,y) plane has a speed u(y) that depends on the distance of the particle from the x-axis. The direction of travel subtends an angle [tex] \theta [/tex] with the x-axis that can be controlled to give the minimum time to move between two points.
Let [tex] u(y) = Ue^{-y/h} [/tex] whereby, U and h are constants.
If the particles starts at (0,0) and has to get to the point [tex](\pi{h}/4,h)[/tex] in the shortest time, show that, the final direction is [tex]\theta = tan^{-1}(e\sqrt{2}-1)[/tex]
A particle travels in the (x,y) plane has a speed u(y) that depends on the distance of the particle from the x-axis. The direction of travel subtends an angle [tex] \theta [/tex] with the x-axis that can be controlled to give the minimum time to move between two points.
Let [tex] u(y) = Ue^{-y/h} [/tex] whereby, U and h are constants.
If the particles starts at (0,0) and has to get to the point [tex](\pi{h}/4,h)[/tex] in the shortest time, show that, the final direction is [tex]\theta = tan^{-1}(e\sqrt{2}-1)[/tex]
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