A bird watcher meanders through the woods, walking 0.50 km due east, 0.80 km due

Question

A bird watcher meanders through the woods, walking 0.50 km due east, 0.80 km due south, and 2.45 km in a direction 31.0° north of west. The time required for this trip is 3.50 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

Explanation / Answer

Represent each of the quantities as vectors, and then you add them up. I will represent the x-component as i and the y-one as j. For the .50 km east, the vector is:

a=.50 i

For the 0.80 km south

b=0.80 (-j)=-0.80 j

For the 31.0° north of west:

c=2.45(cos 31.0°(-i)+sin 31.0° j)
=-2.10 i+1.26 j

and the total displacement will be the sum of the 3 vectorial quantities:

x=a+b+c
=-1.6 i+ 0.46 j

and the vectorial magnitude is determined by the Pythagorean theorem, having the components in x and y:

|x|=sqrt(1.6²+ 0.46²)
=1.66 km

and having the time, you just determine the velocity as the rate of change between displacement and time:

|v|=|x|/|t|
=1.66 km/3.50 h
=0.47 km/h

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