Question

A wildlife researcher is tracking a flock of geese. The geese fly 4.0km due west, then turn toward the north by 40 degrees and fly another 3.5km.

Part A: How far west are they of their initial position?
Part B: What is the magnitude of their displacement?

Answer 1

a.6.68 km

b.7.01 km

Step-by-step explanation:

The gees fly due to west=4.0 km

`\theta=40^(\circ)`

Geese fly another distance due to north=3.5 km

a.We have to find the west distance from their initial position

From below diagram

The x-component of the total distance that geese flies which is the west distance from the initial position

`D_x=4.0+3.5cos40^(\circ)`

`D_x=4.0+2.68=6.68 km`

B. The vertical component of total distance that gees flies from initial position

`D_y=3.5sin40^(\circ)=2.25km`

Magnitude of displacement ,D=
`√(D^2_x+D^2_y)`

Substitute the values then we get

Magnitude of their displacement,D=
`√((6.68)^2+(2.25)^2)=7.01 km`

Magnitude of their displacement,D=7.01 km

Answer 2

(a). The distance from the initial position is 6.68 km.

(b). The magnitude of their displacement is 7.05 km.

Step-by-step explanation:

Given that,

Geese fly 4.0 km due west, then turn to north by 40° and fly another 3.5 km.

(a). We need to calculate the distance from the initial position

Using formula of distance

`D=AB+BC\cos\theta`

Put the value into the formula

`D=4.0+3.5\cos40`

`D=6.68\ km`

(b). We need to calculate the magnitude of their displacement

Using formula of displacement

`AC=√(CD^2+AD^2)`

`AC=√((3.5\sin40)^2+(6.68)^2)`

`AC=7.05\ Km`

Hence, (a). The distance from the initial position is 6.68 km.

(b). The magnitude of their displacement is 7.05 km.