A car is traveling at 130 km/h

Question

A car is traveling at 130 km/h due south at a point 4 /5 kilometer north of an intersection. A police car is traveling at 114 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

The distance between the cars will be the hypotenuse of the right triangle formed: s = sqrt(x_pc² + y_c²) with the origin at the intersection.

We are given dx/dt and dy/dt (-114, -130) in km/hr and x, y (2/5, 4/5) km

In order to find ds/dt, take the derivative of s in terms of t, using chain rule where appropriate:

ds/dt = 1/2 (x²+y²)^-1/2 (2x dx/dt + 2y dy/dt)

Plug it all in. Please check the derivative and all signs...