Plane ride relative motion problem

AI Thread Summary
The problem involves calculating the speed of an airplane relative to the ground, given its velocity with respect to the air and the air's velocity with respect to the ground. The correct approach requires breaking down the velocities into their components using trigonometry. The solution involves using the complementary angle of 120 degrees to accurately calculate the resultant velocity. After applying the Pythagorean theorem to the components, the correct speed of the plane relative to the ground is determined to be approximately 143.95 m/s. A sketch is recommended to aid in visualizing and decomposing the vectors correctly.
clydefrog
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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
(Not so sure about these)

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)

Added to VPA:
236.507 m/s

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

Thanks a lot
 
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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... o_O
 
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clydefrog said:
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... o_O
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.
 
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