Steps for finding a missing vector:
When writing a vector equation for one of these problems, it'll be in a form like
where the missing vector is one of the vectors on the left-hand side of the equation. Note that if the problem is about returning to the starting point, .
For decomposing given vectors, we'll have to define a coordinate system if the problem hasn't, then use the equations
If the final answer is supposed to be in magnitude-angle notation, we'll need to use these equations to get the magnitude and direction:
Step 1. This problem has the plane flying three separate legs (24.0 km at 34.0° south of east, 46.0 km north, and the unknown). We'll call them , , and in order. The resultant is 32.0 km west. So our vector equation is
Step 2. Define a coordinate system so that north is the +y-direction and east is the +x-direction. Then we can decompose vector into x- and y-components. "South of east" in this coordinate system is counterclockwise from the +x-axis, so
You leave the airport in College Station and fly 24.0 km in a direction 34.0° south of east. You then fly 46.0 km due north.
How far must you then fly to reach a private landing strip that is 32.0 km due west of the College Station airport?
In what direction?
Frequently Asked Questions
What scientific concept do you need to know in order to solve this problem?
Our tutors have indicated that to solve this problem you will need to apply the Trig Review concept. You can view video lessons to learn Trig Review. Or if you need more Trig Review practice, you can also practice Trig Review practice problems.
What professor is this problem relevant for?
Based on our data, we think this problem is relevant for Professor Bose's class at UW-MADISON.