A bird watcher meanders through the woods, walking 0.50 km dueeast, 0.75km due s

Question

A bird watcher meanders through the woods, walking 0.50 km dueeast, 0.75km due south, and 2.15km in a direction 35.0onorth of west. The time required for this trip is2.50h. Determine the magnitude and direction (relative to duewest) of the bird watcher's (a) displacement and (b) averagevelocity. Use kilometers and hours for distance and time,repsectively. answer: a)1.35km, 21oN of W             b)0.540kph, 21oN of W A bird watcher meanders through the woods, walking 0.50 km dueeast, 0.75km due south, and 2.15km in a direction 35.0onorth of west. The time required for this trip is2.50h. Determine the magnitude and direction (relative to duewest) of the bird watcher's (a) displacement and (b) averagevelocity. Use kilometers and hours for distance and time,repsectively. answer: a)1.35km, 21oN of W             b)0.540kph, 21oN of W

Explanation / Answer

0.50 km east - 2.15 * cos(35) km west = -1.261 km east (or1.261 km west)
Now, the displacement in the North/South direction is:
0.75 km south - 2.15 * sin(35) km north = -.483 km south (or0.483 km north).
Therefore, the total displacement is given by the pythagoreantheorem: (1.261^2+0.483^2)^(1/2) = 1.35 km.
The angle is given by arctan(0.483/1.261) = 20.96 degrees N ofW.
(b) The average velocity is just the average displacementdivided by the total time = 1.35 km 20.96 degrees North of West / 2.5 = 0.540 kph,20.96 degrees N of W.
Cheers!

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