Phillip R. answered • 08/26/14

Tutor

New to Wyzant
Top Notch Math and Science Tutoring from Brown Univ Grad

with a diagram I get 32 km at an angle 66 degrees north of west

Thuto M.

asked • 08/26/14A vehicle travels 25 km at an angle of 20 degrees north of east, then turns and travels a distance 35 km of at an angle of 50 degrees west of north and finally turns and travels a distance of 10 km at an angle of 10 degrees south of west.

Follow
•
3

Add comment

More

Report

Phillip R. answered • 08/26/14

Tutor

New to Wyzant
Top Notch Math and Science Tutoring from Brown Univ Grad

with a diagram I get 32 km at an angle 66 degrees north of west

Thuto,

First let's specify all angles with respect to the x-axis and determine qualitatively the directions of travel with respect to the x and y axes. It helps to actually graph this as you go and gives you a check on your final answer!

The first direction is already measured with respect to (wrt) the x-axis so we can leave that alone.

The second direction is 50° N or W which is 40° W of N.

The third direction is already measured wrt the x-axis.

Next write the 3 directions in terms of their west **i** components (x-direction) and **j** components (y-direction).

Bold letters indicate vector notation.

The (-) signs indicate that the directions translate into motion to the left (-x) or down (-y)

Now add all the x-components and y-components separately to get the final position.

= -13.2 **i **+ 29.3 **j **km (final position vector)

The displacement is [(-13.2)² + (29.3)²]^{½} = 32 km at an angle of 66° North of West

The last comes from using the x and y-components of the final displacement vector to find tan θ

Ask a question for free

Get a free answer to a quick problem.

Most questions answered within 4 hours.

Find an Online Tutor Now

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.