Susan, driving north at 55 mph, and Shawn, driving east at 45 mph, are approaching an intersection.?

Question

Susan, driving north at 55 mph, and Shawn, driving east at 45 mph, are approaching an intersection. What is Shawn's speed relative to Susan's reference frame?

Answer 1

Gee... and how far apart are they and how close is one of them to the intersection?

Let's say they are D miles apart while Susan distance to intersection is Y while Shaun's is X.

Then D^2=X^2 + Y^2
D=sqrt(X^2 + Y^2)

Also let dD/dt be Shawn's speed relative to Susan's reference frame and

Then
dD/dt=[1/sqrt(X^2 + Y^2)][X dX/dt + Y dY/dt]
where
dX/dt= - 45 mph
dy/dt= 55 mph