Question

A bird watcher meanders through the woods, walking 0.45 km due east, 0.65 km due south, and 2.90 km in a direction 32.0° north of west. The time required for this trip is 2.00 h.

(a) Determine the magnitude and direction (relative to due west) of the bird watcher's displacement. Use kilometers and hours for distance and time, respectively.

magnitude _______________ km

direction _______________ ° north of west

(b) Determine the magnitude and direction (relative to due west) of the bird watcher's average velocity.

magnitude ____________ km/hr

direction _____________ ° north of west

Answer 1

As we know that

Break each segment into west and north components. south is negative north, east is negative west.
Add all of the west components together and all of the north components together.
Use pythagoras to determine the magnitude of the result.
trigonometry to find the angle.
north and west are the positive directions

leg one
distance is 0.45 km
direction is due east, no other components
this can be written -0.450 km west

leg two
distance is 0.65 km
direction is south, no other components
can also be written -0.65 km north

leg three
north component is 2.90 sin 32 = 1.536765866 km
west component is 2.90 cos 32 = 2.459339479 km

total north displacement is 1.536765866 - 0.65 = 0.886765866 km
total west displacement is 2.459339479 - 0.450 = 2.009339479 km

magnitude of displacement is
(0.886765866^2 + 2.009339479^2)^0.5 = 2.196314833 km

direction is
tanθ = (0.886 / 2.009)
θ = 23.81 degrees north of west

the average velocity is the total displacement over the total time
v = 2.196314833 / 2 = 1.098157417 km/hr