Vectors, Direction, and Net displacement

In summary, The speaker is seeking help with two problems involving distance and direction. The first problem involves a helicopter traveling northwest 70.7 miles, then east 100 miles, and finally south 100 miles. The second problem involves a ship sailing 100 miles northwest and then 141.4 miles south. The speaker has provided calculations for the second problem but is unsure if they are correct.
  • #1
rorushing4283
2
0
I have been working on the following two problems and I can't seem to get any progress.
Any help from anyone would be greatly appreciated. I know it seems simple to those who are familiar but I have no background in this type of equations.

1. A helicopter travels northwest 70.7 miles, then straight east 100 miles, and finally straight south 100 miles. How far and in what direction is it from point of origin?



2. A ship sails 100 miles northwest then 141.4 miles due south. How far and in what direction is it from its starting location?
 
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  • #2
for 2

100 miles NW
141.4 miles S

x=100cos135=-70.71
y=100sin135=70.71

Mag=sqrt(-70.71)^2+(70.71)^2
Mag=sqrt10000
Mag=100miles

is this on the right track for this problem?
 

FAQ: Vectors, Direction, and Net displacement

What is a vector?

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

How is direction represented in a vector?

Direction in a vector can be represented in different ways, such as using angles or compass directions. In two-dimensional vectors, direction can be represented using the trigonometric functions of sine and cosine.

What is the difference between displacement and net displacement?

Displacement is the distance and direction between an object's initial position and its final position. Net displacement, on the other hand, is the overall distance and direction of an object's movement, taking into account any changes in direction or magnitude during its motion.

How are vectors added or subtracted?

Vectors can be added or subtracted using the head-to-tail method or by breaking them down into their horizontal and vertical components. The resulting vector will have a magnitude and direction that is dependent on the original vectors.

How are vectors used in real-life applications?

Vectors are used in a variety of real-life applications, such as navigation, engineering, and physics. They are particularly useful for calculating forces, velocities, and accelerations in both two-dimensional and three-dimensional systems.

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