# Plane ride relative motion problem

## Homework Statement

You are traveling on an airplane. The velocity of the plane with respect to the air is 160 m/s due east. The velocity of the air with respect to the ground is 41 m/s at an angle of 30° west of due north.

1) What is the speed of the plane with respect to the ground?

## Homework Equations

VAB=VAC+VBC
Pythagorean theorem
Trigonometry

## The Attempt at a Solution

I know that VPG=VPA+VAG, but I'm not sure about how to break velocities into their components.
I kept VPA at 160 since it only moves in one dimension (only east), and I tried breaking up VAG as such:

41cos60i+41sin60j

(60 degrees since that is the angle formed when putting VAG tip to tail with VPA)

236.507 m/s

In searching various forums (this seems a common hw question), I've seen very different solutions than mine, so I know mine is wrong.

Thanks a lot

Last edited:

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OK so I tried using the complementary angle of 120, and then added the i (160 + 41cos120) and j (41sin60) components, then put each into the Pythagorean theorem

VPG=√(i-components2 + j-components2) = 143.9479, which is the right answer

I'm unsure as to why 120 was the right angle to use... Last edited:
SteamKing
Staff Emeritus
Homework Helper
OK so I tried using the complementary angle of 120, and then added the i (160 + 41cos120) and j (41sin60) components, then put each into the Pythagorean theorem

VPG=√(i-components2 + j-components2) = 143.9479, which is the right answer

I'm unsure as to why 120 was the right angle to use... Always make a sketch. These are quite useful in showing how to decompose vectors into their components.

Remember,to decompose a vector into its unit vector components in i and j, due east represents a heading angle of 0 degrees.

Thanks, the confusion turned out to be coming from a bad drawing.