A bird watcher meanders through the woods, walking 0.40 km due east, 0.60 km due
ID: 1880935 • Letter: A
Question
A bird watcher meanders through the woods, walking 0.40 km due east, 0.60 km due south, and 2.00 km in a direction 42.0° north of west. The time required for this trip is 4.00 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
Explanation / Answer
here,
s1 = 0.4 i km
s2 = - 0.6 j km
s3 = 2 km * ( - cos(42) i + sin(42)j)
s3 = - 1.49 i km + 1.34 j km
time required , t = 4 hr
a)
the net dispacement , s =s1 + s2 + s3
s = 0.4 i km - 0.6 j km - 1.49 i km + 1.34 j km
s = - 1.09 i km + 0.74 j km
the magnitude of displacement , |s| = sqrt(1.09^2 + 0.74^2) km
|s| = 1.32 km
direction , theta = arctan(0.74/1.09) = 34.2 degree north of west
b)
the bird watcher's average velocity , v = |s| /t
v = 1.32/4 km/h = 0.33 km/h
the direction of average velocity is 34.2 degree north of west