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April 16, 2014

April 16, 2014

Posted by **RE** on Thursday, September 10, 2009 at 8:34pm.

(a) At the turning point, how far is the second cyclist from the campground?

(blank) m

(b) What direction (measured relative to due east) must the second cyclist head during the last part of the trip?

(blank)° (blank = either north or south) of east

- Physics -
**MathMate**, Thursday, September 10, 2009 at 9:21pmResolve the displacements into East (x) and North (y) components.

First find the coordinates of the campground relative to the starting point:

Distance angle x-component y-component

1490 0° 1490cos(0) 1490sin(0)

1430 90° 1430cos(90) 1430sin(90)

Total ---- 1490 1430

Therefore the campground is at (1490,1430) relative to the starting point.

At the turning point, the second cyclist is at (0,2130) relative to the starting point.

The distance from the campground is therefore the distance between the two points (0,2130) and (1490,1430).

The direction of P2(x2,y2) from P1(x1,y1) is atan2(y2-y1, x2-x1), taking into account of the signs of the values and therefore the quadrant.

In the case in point, the angle is

atan2(1430-2130,1490-0) = -25 degrees approximately, or 25 degrees south of east.

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