Determine the magnitude and direction of the bird watchers displacement. ?

Question

A bird watcher meanders through the woods, walking 0.30 km due east, 0.70 km due south, and 2.65 km in a direction 31.0 degrees north of west. The time required for this trip is 2.50 h.

A.) Determine the magnitude and direction of the bird watchers displacement.

magnitude_______km

direction________degrees north of west

B.) Determine the magnitude and direction of the bird watcher's average velocity.

magnitude_________km/hr

direction_________degrees north of west

Answer 1

The displacement east is:

x = 0.30 - 2.65 cos(31)

= - 1.9715 km.

The displacement north is:

y = - 0.70 + 2.65 sin(31)

= 0.6649 km.

(a)

The magnitude of the displacement is:

sqrt(x^2 + y^2)

= 2.08 km. to 3sf.

The direction of the displacement is angle a north of west, where:

tan(a) = 0.6649 / 1.9715

a = 18.6 deg.north of west.

(b)

Dividing the displacement by the time 2.50 hr, the average velocity has magnitude:

sqrt(x^2 + y^2) / 2.50

= 0.832 km/hr.

Its direction is the same as that of the displacement:

18.6 deg. north of west.