A bird watcher meanders through the woods, walking 0.744 km due east, 0.925 km due south, and 3.97 km in a direction 18.3 ° north of west. The time required for this trip is 1.765 h. Determine the magnitudes of the bird watcher's (a) displacement and (b) average velocity.
a. D=0.744[0o] + 0.925[270o] + 3.97[161.7o] CCW.
X = 0.744+0.925*Cos270+3.97*Cos161.7 =
0.744 + 0 - 0.949 = - 0.205 km.
Y = 0 + 0.925*sin270 + 3.97*sin161.7 =
0 - 0.925 + 1.25 = 0.325 km.
Tan A = Y/X = 0.325/-0.205 = -1.58537.
A = -57.8o = 57.8o N. of W. = 122.2o CCW
D=Y/sinA=0.325/sin122.2=0.384 km[57.8o N
of W.] = Displacement.
b. V = (d1+d2+d3)/T = (0.744+0.925+3.97)/1.765=
3.19 km/h.
To determine the magnitudes of the bird watcher's displacement and average velocity, we need to break down the given information.
(a) Displacement:
The displacement is the straight-line distance between the bird watcher's initial and final positions. We can find the displacement by using vector addition.
1. Convert the direction of 3.97 km north of west to its components:
- The west component will be 3.97 km * cos(18.3°).
- The north component will be 3.97 km * sin(18.3°).
2. Add up all the components:
East component = 0.744 km
South component = -0.925 km
West component = -3.97 km * cos(18.3°)
North component = 3.97 km * sin(18.3°)
The total displacement is the vector sum of these components.
Displacement = √((East component)^2 + (North component)^2)
(b) Average Velocity:
Average velocity is the total displacement divided by the time taken.
1. Calculate the total displacement as obtained earlier.
2. Divide the total displacement by the time taken:
Velocity = Displacement / Time
Now, let's compute the magnitudes of the bird watcher's displacement and average velocity:
Step 1: Convert the direction of 3.97 km north of west to its components:
West component = 3.97 km * cos(18.3°)
North component = 3.97 km * sin(18.3°)
Step 2: Calculate the total displacement:
Displacement = √((0.744 km + West component)^2 + (-0.925 km + North component)^2)
Step 3: Calculate the average velocity:
Velocity = Displacement / 1.765 h
Now you can plug in the values into the above formulas and perform the calculations to find the magnitudes of the bird watcher's displacement and average velocity.