While doing some biological field work you park your car at the western end of a
ID: 1586435 • Letter: W
Question
While doing some biological field work you park your car at the western end of an east-west dead-end forest road. From there you set off on foot to collect data at three locations within your study area. Let the +x direction be east, and the +y direction be north. To get to the first site, you hike 825 m directly south (vector A). After collecting data there you take vector B to the next site, 1.25 km away in a direction 30.degree west of north (or alternatively, a bearing of 330degree clockwise from north). Finally, taking vector C 1.00 km in a direction 40.degree north of cast (a bearing of 50degree clockwise from north) brings you to your last site. After finishing recording your data and notes, it's time to head back, (a) Use mathematical vector addition to find the distance and direction back to the car (vector D). Note that your total displacement when you get back to the car is Ar = A + B + C + D = 0. (b) Check your calculations with a graphical solution drawn roughly to scale.Explanation / Answer
a )
A = -825 j
B = -625i + 1082.53 j
C = 766.044 i + 642.78 j
we know that
A+B+C+D = 0
therefore substituting values we get
D = -141.044 i -900.31 j
Magnitude of D
D = 911.306
direction 81.096 degree south of west
theta =
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