# Displacement and vector problems

• Spartanlol
In summary, the plane's total displacement is 174 km. The plane's displacement at an angle east of north is 158.33 km.
Spartanlol
Ok, so I am having a difficult time with vectors (despite the fact that it appears to be an easy concept). My main issue is I am so focused on my AP Calc and AP English classes that I have not had much time for any studying, so I rely on what I hear during the course. I am required to complete this assignment and it is worth 60% of my grade, and part of it is on Vectors. That being said, I am in need of help to understand this. If you do not feel like answering some of these, any advice would be greatly appreciated on HOW you would solve a question of that sort. I will provide all of the questions (or if there are multiple questions with same basic concept, I will just show 1) and all of my work up to where I get lost. Thanks in advance!

1. A plane travels 2.0 km at an angle of 33◦ to the
ground, then changes direction and travels 7.7
km at an angle of 18◦ to the ground.
What is the magnitude of the plane’s total
displacement?
Answer in units of km. At what angle above the horizontal is the
plane’s total displacement?

-For this particular question, I am stuck. For some reason, I am not understanding how to do this...

2. An airplane flying parallel to the ground un-
dergoes two consecutive displacements. The
first is 33 km at 18.3◦ west of north, and the
second is 174 km at 65.5◦ east of north.
What is the magnitude of the plane’s total
displacement?
Answer in units of km. At what angle east of north is the plane’s total
displacement?

-After calculating the side (hypotenuse) I got 158.33 but it was wrong

3. A quarterback takes the ball from the line
of scrimmage, runs backward for 15.0 yards,
then runs sideways parallel to the line of
scrimmage for 15.0 yards. At this point,
he throws a 21.0-yard forward pass straight
down the field.
What is the magnitude of the football’s
resultant displacement?

-Now this one I am lost on. I had this on a quiz a few days back and missed it. I set it up to where there is a triangle with one side being 6 (6 left over from the 21 yrd pass past the 15yrds where it started) and the other side being 15 (when making it a right triangle). Then I did a^2+b^2=c^2 and got 16.15. I believe that is right but I am afraid to answer before making sure.

4. The eye of a hurricane passes over Grand
Bahama Island. It is moving in a direction
57.2◦ north of west with a speed of 34.6 km/h.
Exactly 2.97 hours later, the course of the
hurricane shifts due north, and its speed slows
to 28.8 km/h, as shown.
How far from Grand Bahama is the hurri-
cane 4.23 h after it passes over the island?

-Got really lost on this one. I would assume you would first subtrade 2.97 from 4.23, then times that by 28.8 to get the distance then find the hypotenuse?

5. A submarine dives 185.0 m at an angle of
13.0◦ below the horizontal.
What is the horizontal component of the
submarine’s displacement?
Answer in units of m.What is the vertical component of the subma-
rine’s displacement?

Update**
.
For #1 I think I found the solution. I made the triangle and split it into a right triangle and got 2tan36 which is 1.45 and the angle of it would be 72 degrees?

Edit: My answer was wrong >.<..im clueless

Last edited:

Could really use help..this is due in 2 hours and I am completely stuck. I have already answered them all 3 times with different answers that are all wrong. I don't even mind if you won't give answer but some help on HOW to get answer would be MUCH appreciated!

## 1. What is displacement?

Displacement is a vector quantity that measures the change in position of an object from its starting point to its ending point. It is a straight line distance between the two points and is typically represented by an arrow with both magnitude and direction.

## 2. How is displacement different from distance?

Distance is a scalar quantity that measures the total amount of ground covered by an object, regardless of direction. Displacement takes into account the direction of movement and is therefore a vector quantity.

## 3. What is a vector in relation to displacement?

A vector is a mathematical representation of a physical quantity that has both magnitude and direction. In the case of displacement, the vector represents the change in position of an object from its starting point to its ending point.

## 4. How is displacement calculated?

Displacement can be calculated by subtracting the initial position of an object from its final position. This results in a vector with both magnitude and direction. Alternatively, displacement can be calculated using the Pythagorean theorem if the direction and length of the displacement vector are known.

## 5. What are some real-world examples of displacement and vector problems?

Examples of displacement and vector problems include calculating the displacement of a car traveling along a curved path, determining the overall displacement of a person walking in a park, and finding the displacement of a ball thrown at an angle. These types of problems are commonly encountered in physics, engineering, and navigation.

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