Differential · Integral · Statics

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Related rates — worked solution
x2+y2=L2
2xdxdt+2ydydt=0
dydt=xydxdt
x = 3,  y = 4,  dx/dt = 0.5
dydt=0.375 m/s
A 5-metre ladder rests against a wall. Its base is x metres from the wall and its top is y metres up. From x squared plus y squared equals L squared, differentiating with respect to time gives 2x times dx/dt plus 2y times dy/dt equals 0, so dy/dt equals minus x over y times dx/dt. With x equals 3, y equals 4 and dx/dt equals 0.5 metres per second, the top of the ladder falls at 0.375 metres per second.
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