A hiker begins a trip by first walking 23.0 km southeast from her base camp. On

Question

A hiker begins a trip by first walking 23.0 km southeast from her base camp. On the second day she walks 45.0 km in a direction 60.0? north of east, at which point she discovers a forest ranger's tower.

(a) Determine the components of the hiker's displacements in the first and second days.

Ax = km

Ay = km

Bx = km

By = km

(b) Determine the components of the hiker's total displacement for the trip.

Rx = km

Ry = km

(c) Find the magnitude and direction of the displacement from base camp.

Magnitude = km

Direction = ? north of east

Explanation / Answer

let +y=north and +x=east from the origin draw a line 25 units at 45 deg below +x (45 SofE) from the end of that line draw a line 40 units 60 deg up from horizontal (60 deg NofE) connect the origin to the end of the second line you now have a triangle use trig to find the magnitude and direction of this resultant I use a calculator which adds vectors directly so I enter 25?-40+ 40?+60 and get about 39?38 or 39 km 38 deg N of E

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