Question 1160501: A jet is flying at 350 miles/hour in still air. It is traveling in the direction of 210°, where 90° represents North. Find the component form of vector r, which represents the jet's motion.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
Since I'll be using the letter r below for something else, I'll rename "vector r" into "vector v".
A vector v is in the form v = < x, y > to tell us the x and y offset. It's basically a guide to tell you how to move from one point to another.
x and y are defined as such
x = r*cos(theta)
y = r*sin(theta)
where r is the magnitude of the vector (aka vector length) and theta is the direction (aka argument)
In this case, r = 350 and theta = 210
x = r*cos(theta) = 350*cos(210) = -303.108891324553
y = r*sin(theta) = 350*sin(210) = -175
Make sure your calculator is set to degree mode.
Answer is approximately < -303.108891324553, -175 >
Round however you need to, or however your teacher instructs.
Side note: The vector < -303.108891324553, -175 > represents the idea that the plane is traveling roughly 303.108891324553 mph west and 175 mph south at the same time.
Another side note: There is no mention of the wind, and you state that the plane's speed in still air is 350 mph. Keep in mind that wind will play a factor in real world scenarios. For this problem however, we just ignore it for the sake of simplicity.
|
|
|
