# Math Help - Travelling along...

1. ## Travelling along...

We have a circle radius=25 miles, with center at origin.
Traveller A is on circle's circumference, at A(20,15).
Traveller B is on x axis, at B(39,0).
They leave at same time, A travelling along the circumference counter clockwise,
B travelling in a straight line, such that A and B arrive at point P(u,v) on the
circle's circumference at same time.

QUESTION:
if the speeds of A and B are given, what is "easiest" way to calculate u and v?
Say the speeds are A = a mph, B = b mph.

2. Originally Posted by Wilmer
We have a circle radius=25 miles, with center at origin.
Traveller A is on circle's circumference, at A(20,15).
Traveller B is on x axis, at B(39,0).
They leave at same time, A travelling along the circumference counter clockwise,
B travelling in a straight line, such that A and B arrive at point P(u,v) on the
circle's circumference at same time.

QUESTION:
if the speeds of A and B are given, what is "easiest" way to calculate u and v?
Say the speeds are A = a mph, B = b mph.
Convert to polars and express the speeds as angular velocities.

CB

3. Thanks CB. That's too easy!!

I should have stated the HOW that I'm after.
1: get length BP (make it m)
2: get length arcAP : simple nuff: a/b(length BP)
3: get length chordAP (make it n)
4: calculate u,v using m and n

Reason for doing it that way: that's the level person I'm helping is at.
In this example, a nice point P to use (integer coordinates) would be P(7,24);
by "nice point P", I mean a point to "show how it works"....