# Angles and rates of change

I'm trying to get my head around the following problem, any help is appreciated. My maths skills aren't the best, so apologies in advanced for its stupidity.

Say I'm in a car, and I'm driving directly towards a stationary car (Car A) at 5 meters per second. Every second I get 5 meters closer to Car A, obviously.

Now, say there's another stationary car behind me (Car B) to the right at a 45 degree angle. Every second I measure my distance to Car B, as well.

My rate of change to Car A is consistent at 5 meters per second, yet, correct me if I'm wrong, my rate of change to Car B varies from second to second. For every second measured, my distance to Car B has changed by a different increment, as compared to the previous measurement. It's not a smooth change, second by second.

Why is this? What is it about the angles that causes my rate of change to Car A to be consistent, but my rate of change to Car B to differ?

Many thanks for any clarification,

Steven

• Use the fact that the distance between two points $A(x_1,y_1)$ and $B(x_2,y_2)$ is given by $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$. – Hussain-Alqatari Sep 15 '19 at 13:09

## 1 Answer

Think how you measuring angle. Now Cars are travelling in 2 D dimension (Since cars don't fly) angle $$tan \theta = \frac{y-distance-difference}{x -distance -difference}$$. Assume your car (say P) starts by origin and car A at some where at Y axis and car B is on $$y=tan({\pi \over 4}) .x$$ . Now you if you see after some time x distance is constant from car P to A and it is zero , that's why angle is constant and it is also zero. but if you see both distances from car B are changing.