Related rates for calculus 1finding speed

Question

Two cars are moving towards an intersection. One car is meters north of the intersection and moving towards the intersection at m/s, while the other is meters west of the intersection and moving away from the intersection at m/s. How rapidly are the cars approaching each other seconds later? Please show detailed solution and round answer to 3 decimal places.



Answer 1

The diagram is of a right triangle with y units north and x units west. Both velocities are negative as y approaches from North to South, and the x is negative as it moves from the intersection East to West.

In the right triangle, x² + y² = h² where h is the hypotenuse of the triangle or the distance between x and y. Taking the derivative of this equation yields 2xx' + 2yy' = 2hh' where ' is the velocity indicator and h is the hypotenuse.

Thus - xx'-+ yy' = hh' and h' = (-xx' - yy')/(x² +y²)^1/2 but they are not approaching each other.