Vectors and resultant vectors?

In summary, there is a discrepancy in the rule used to calculate the x and y components of the displacement for an airplane flying west of north. While using the positive x-axis, rsinθ equals to x and rcosθ equals to y, but when using the positive y-axis, this rule is reversed.
  • #1
madinsane
32
0

Homework Statement



An airplane starting from airport A flies 300 km east, then 350 km at 30.0" west of north, and then 150 km north to arrive finally at airport B. The next day, another plane flies directly from A to B in a straight line. In what direction should the pilot travel in this direct flight?

I actually solved it... I drew the vectors and got the resultant displacement.
so its 300i
150j
and then we use rsinθ and rcosθ to get the x and y components of west of north. At first I used rcosθ to get x and rsinθ to get y but that turned out to be wrong (it was actually rsinθ that equaled to x and rcosθ equal to y)
That is what I don't get!
How come the rule here is reversed?
Thanks


The Attempt at a Solution

 
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  • #2
madinsane said:

Homework Statement



An airplane starting from airport A flies 300 km east, then 350 km at 30.0" west of north, and then 150 km north to arrive finally at airport B. The next day, another plane flies directly from A to B in a straight line. In what direction should the pilot travel in this direct flight?

I actually solved it... I drew the vectors and got the resultant displacement.
so its 300i
150j
and then we use rsinθ and rcosθ to get the x and y components of west of north. At first I used rcosθ to get x and rsinθ to get y but that turned out to be wrong (it was actually rsinθ that equaled to x and rcosθ equal to y)
That is what I don't get!
How come the rule here is reversed?
Thanks


The Attempt at a Solution


Perhaps you just mechanically use rsinθ that equaled to x and rcosθ equal to y when you are comparing to the positive x-axis - (or the only polar axis)
 

1. What is a vector?

A vector is a physical quantity that has both magnitude and direction. It is represented by an arrow pointing in the direction of the vector, with the length of the arrow representing the magnitude.

2. How do you calculate the magnitude of a vector?

To calculate the magnitude of a vector, you can use the Pythagorean theorem. This involves squaring each component of the vector, adding them together, and then taking the square root of the sum.

3. What is a resultant vector?

A resultant vector is the vector that represents the sum of two or more vectors. It is found by placing the vectors head-to-tail and drawing a new vector from the tail of the first vector to the head of the last vector.

4. How do you find the direction of a resultant vector?

The direction of a resultant vector can be found by using trigonometric functions. The angle of the resultant vector can be calculated using the inverse tangent function, or by using the dot product and the inverse cosine function.

5. Can vectors be added or subtracted?

Yes, vectors can be added or subtracted using the parallelogram rule. This involves drawing parallelograms with the vectors as sides, and the diagonal of the parallelogram represents the resultant vector.

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