A car is traveling at 79 km/h

Question

A car is traveling at 79 km/h due south at a point 4/5kilometer north of an intersection. A police car

 is traveling at 63 km/h due west at a point 2/5 kilometer due east of the same intersection.At that

 instant, the radar in the police car measures the rate at which the distance between the two cars is changing. What does the radar gun register?

Answer 1

if x is the distance between the police car and the intersection, and y is the distance between the other car and the intersection, then dx/dt=-63 km/h and dy/dt=-79 km/h. For L=the distance between the two cars, L^2=x^2+y^2.

Use implicit differentiation to find dL/dt at x=0.8 km and y=0.4 km (==> L^2=0.4^2+0.8^2 ==> L=sqrt(0.8)).