Question

Find the resultant displacement of a bear searching for berries on the mountain. The bear heads 55.0º north of west for 15.0 m; then it turns and heads to the west for another 7.00 m. (Use trigonometry to answer, but remember to draw a diagram to help your understanding.)

Answer 1

North component: y = 15.0 m * sin 55.0º = 12.3 m
West component: x = 15.0 m * cos 55.0º + 7.00 m = 15.6 m

so his heading, measured from West, is
Θ = arctan(y/x) = arctan0.787 = 38.2º N of West

and measured from North is
φ = arctan(x/y) = arctan(1.27) = 51.8º W of North

Hope this helps!

Answer 2

Resultant, d = 19.9 meters

Step-by-step explanation:

It is given that,

The bear heads 55 degrees north of west for 15.0 m; then it turns and heads to the west for another 7.00 m. The attached figure shows the whole scenario.

The net displacement of bear due north is given by :

`d_n=15\ sin\theta`

`d_n=15\ sin(55) = 12.28\ m`

The net displacement of bear due west is given by :

`d_w=15\ cos\theta+7`

`d_w=15\ cos(55)+7=15.60\ m`

Let d is the resultant displacement of a bear searching for berries on the mountain. It can be calculated as :

`d=√(d_n^2+d_w^2)`

`d=√(12.28^2+15.60^2)`

d = 19.85 meters

or

d = 19.9 meters

So, the resultant displacement of a bear is 19.9 meters. Hence, this is the required solution.