Question

A bird watcher meanders through the woods, walking 1.93 km due east, 1.03 km due south, and 3.84 km in a direction 52.8 ° north of west. The time required for this trip is 1.771 h. Determine the magnitudes of the bird watcher's (a) displacement and (b) average velocity.

Answer 1

To determine the bird watcher's displacement, we can find the result of adding the individual displacements using vector addition. The average velocity is the total displacement divided by the total time taken.

Step-by-step explanation:

To determine the bird watcher's displacement, we can find the result of adding the individual displacements using vector addition. The displacement is the straight-line distance and direction from the initial position to the final position. We can use the Pythagorean theorem and trigonometry to find the magnitude and direction.

For the bird watcher's displacement, we can find the north and east components of each displacement using trigonometry. Then we can add the north components and the east components separately to get the total north and east displacement. Finally, we can use trigonometry again to find the magnitude and direction of the total displacement.

The average velocity is the total displacement divided by the total time taken. We can calculate this by dividing the magnitude of the displacement by the time taken.

Answer 2

Magnitude of displacement = 2.07 km

Magnitude of average velocity = 1.17 kmph

Step-by-step explanation:

Let east represent positive x axis and north represent positive y axis.

A bird watcher meanders through the woods, walking 1.93 km due east, 1.03 km due south, and 3.84 km in a direction 52.8 ° north of west.

1.93 km due wast

s ₁ = 1.93 i km

1.03 km due south

s₂ = -1.03 j km

3.84 km in a direction 52.8 ° north of west

s₃ = -3.84 cos 52.8 i + 3.84 sin 52.8 j = -2.32 i + 3.06 j km

Total displacement

s = s ₁+ s₂+ s₃ = 1.93 i - 1.03 j -2.32 i + 3.06 j = -0.39 i + 2.03 j

Magnitude of displacement,
`=√((-0.39)^2+2.03^2)=2.07km`

Time taken = 1.771 hour

Magnitude of average velocity,
`=(2.07)/(1.771)=1.17km/hr`