A police car is after a speeding SUV that has turned a corner and is now moving straight east as it approaches the right-angled intersection from the north. When the police car is 0.6 kilometers north of the crossing and the SUV is 0.8 kilometers east of the intersection, the police use radar to calculate that gap between them and the SUV is growing at a rate of 20 kilometers per hour. What is the speed of the SUV if the police car is traveling at 60km/hr at the time of measurement?
the distance z is
z^2 = x^2 + y^2
z dz/dt = x dx/dt + y dy/dt
at the given moment, we have
1*20 = .6(-60) + .8 dy/dt
dy/dt = 70 km/hr