be the distance of the vehicle heading West from the origin. Express c in terms of x and y via the Pythagorean theorem: Express dc/dt using chain rule in terms of dx/dt and dy/dt: Substitute in x = 4 mi, y = 3 mi, dx/dt = −80 mi/hr, dy/dt = 60 mi/hr and simplify Consequently, the two vehicles are getting closer together at a rate of 28 mi/hr. Electromagnetic induction of conducting loop spinning in magnetic field The magnetic flux through a loop of area A whose normal is at an angle θ to a magnetic field of strength B is Faraday's law of electromagnetic induction states that the induced electromotive force is the negative rate of change of magnetic flux through a conducting loop. If the loop area A and magnetic field B are held constant, but the loop is rotated so that the angle θ is a known function of time, the rate of change of θ can be related to the rate of change of (and therefore the electromotive force) by taking the time derivative of the flux relation If for example, the loop is rotating at a constant angular velocity ω, so that θ = ωt, then References Differential calculus Differential equations