Vector Addition for Displacement: Finding Magnitude and Direction

In summary, the problem involves a car being driven first 125km west and then 95km southwest. The magnitude and direction of displacement is asked for. The triangle method can be used to solve this problem by splitting the displacements into west and south components and adding them separately. The angle can be found by using arctan. It is assumed that when the direction is given as southwest, it means exactly 45 degrees between west and south. The final answer would be 95sin45km west and 95cos45+125km south, with a magnitude of sqrt[(95sin45)^2+(95cos45+125)^2] and an angle of arctan (abs value[(95sin45)/(125+
  • #1
alandry06
11
0

Homework Statement


I am not sure where I am having trouble here.

A car id driven 125km west and then 95km southwest. What is the mag and direction of displacement?

Homework Equations


Triangle method says that if I draw the vectors from tip to tail, the displacement vector is the vector that connects the tail of the first vector to the head of the last one.

The Attempt at a Solution

I am assuming (hopefully correctly!) that magnitude is just 230km, but I cannot sem to find direction.

If it were 125 west and 95 south of west I could figure it out, but it is 125 west and 95 southwest...so I can't use arctan can I?
 
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  • #2
Wait...after looking at it again, I think the magnitude is wrong too...
 
  • #3
It probably isn't correct. Split both displacements into west and south components using sin and cos. Then add the west and south components separately. Finally, you use arctan.
 
  • #4
Dick said:
It probably isn't correct. Split both displacements into west and south components using sin and cos. Then add the west and south components separately. Finally, you use arctan.

I thought of that but I am not given any angles?
 
  • #5
95km southwest is 95*sin(45)km west plus 95*sin(45)km south. Does that help? Your final displacement should be mostly west and some south. How much of each? So for an angle you could just say how many degrees south of west is it.
 
  • #6
Wait...is it safe to assume that when they say southwest they mean exactly 45 degrees between west and south?...I am going to bank on that being the case.

Edit:Thanks Dick! It took me awhile to type that...but it appears you confirmed my idea. I should be able to get this from here.
 
  • #7
So (95sin45)^2+(95cos45+125)^2=mag and the angle would be
arctan (abs value[(95sin45)/(125+95cos45)]) south of west.
 
  • #8
Right. Except that's mag^2. Don't forget the sqrt.
 

FAQ: Vector Addition for Displacement: Finding Magnitude and Direction

What is vector addition?

Vector addition is a mathematical operation that involves combining two or more vectors to produce a new vector. The resulting vector represents the sum of the magnitudes and directions of the individual vectors.

What are the properties of vector addition?

Vector addition has three main properties: commutativity, associativity, and distributivity. Commutativity means that the order of the vectors being added does not change the result. Associativity means that the grouping of vectors being added does not change the result. Distributivity means that multiplying a vector by a scalar and then adding it to another vector is the same as adding the two vectors separately and then multiplying the sum by the scalar.

How is vector addition visualized?

Vector addition can be visualized using a graphical method known as the head-to-tail method. This involves drawing the first vector with its tail at the origin and its head at a designated point. Then, the second vector is drawn with its tail at the head of the first vector, and its head at a new designated point. The resulting vector from the origin to the head of the second vector represents the sum of the two vectors.

What is the difference between vector addition and scalar addition?

Vector addition involves combining both the magnitude and direction of vectors, while scalar addition only involves combining the magnitudes. Scalar addition is essentially just adding numbers, while vector addition takes into account the direction of the vectors being added.

How is vector addition used in science?

Vector addition is used in various fields of science, including physics, engineering, and navigation. It is used to calculate the net force on an object, the resultant displacement of an object, and the velocity of an object. It is also used in calculating the direction and magnitude of forces in complex systems, such as in electrical circuits or in fluid mechanics.

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