A hiker begins a trip by first walking 23.5 km southeast from her base camp. On

Question

A hiker begins a trip by first walking 23.5 km southeast from her base camp. On the second day she walks 43.0 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.

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

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

A cruise ship leaving port travels 46.0 km 45.0° north of west and then 66.0 km at a heading 30.0° north of east.(a) Find the components of the ship's displacement vector.

(b) Find the displacement vector's magnitude and direction.

Explanation / Answer

1.(a). Displacement A has a magnitude of 23.5 km and is directed 45.0 deg below the positive x axis

Ax = 23.5*cos(-45) = 16.617 km

Ay = 23.5*sin(-45) = -16.617 km

The second displacement B has a magnitude of 43.0 km and is 60.0 deg north of east. Its components are

Bx = 43*cos(60) = 21.5 km

By = 43*sin(60) = 37.23 km

(b) Rx = Ax + Bx = 16.617 + 21.5 = 38.117 km

Ry = Ay + By = -16.617 + 37.23 = 20.613 km

(c) magnitude R = (38.117^2 + 20.613^2)^0.5 = 43.333 km

direction = arctan(20.613/38.117) = 28.40 deg

2. (a)  Rx = -46*cos(45) +66*cos(30) = -32.526 + 57.157 = 24.631 km

(note the first vector point to the left while the second vector points to the right)

Ry = 46*sin(45) +66*sin(30) = 32.526 + 33 = 65.526
R= (24.631^2 + 65.526^2)^0.5 = 70.00 km

Direction = arctan(65.526/24.631) = 69.39 deg

comment below if you have further doubt

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