Basic vector addition - my attempts

In summary, the teacher does not want this homework back, I just want to learn because I love science.
  • #1
victorhugo
127
5
The teacher does not want this homework back, I just want to learn because I love science
"1) A golf ball at a mini golf course is hit 10m NE where it hits a barrier and travels NW for another 18m. What is the balls displacement from the tee?"
square root(18^2)+(10^2)= 20.6 metres. Now for the angle I am confused, using SOH CAH TOA I always get 61 degrees, but apparently its N 15.9 W, could someone please show me why?

"5) A duck is realeased onto a lake and swims due west across it for 50 m, it then turns a swims due North for 2m. What is its displacement from its realse point?"
The displacement squared is (2^2 + 50^2) = 2504, square rooting it the displacement is 50m
For the angle,(using tan=opp./adj., opposite to the angle is 2 and adjacent ot it is 50), tan^1(2/50) = 2.3
The displacement of the duck is then 50m West 2.3° North"8) During the hammer throw at the Australian trials a hammer left the cafe traveling at 90km/h due south into a cross wind which blew it due west at 2km/h. What is its relative velocity ov the ground?"
I'm cnfused with this one, but I think that we can get it by using r^2=a^2+b^2 but making it so that the 2km/h of the wind is negative, so the square root of (-2^2) + (90^2) = 89.9m/s

 
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  • #2
1. That is correct.
You need to subtract 45o to get how much to the west of north the direction lies (it helps to make a drawing).
 
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  • #3
andrevdh said:
1. That is correct.
You need to subtract 45o to get how much to the west of north the direction lies (it helps to make a drawing).
Ohh okay, but why do i need to subtract 1/8 of 360 to get my answer? what is the logic behind it?
 
  • #4
see drawing
 

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  • #5
andrevdh said:
see drawing
Ohhh I get it, I'm sorry I have little to no knowledge on graphs/angles so I didn't know what was going on... By looking at your picture I see that when the ball went 10m NE it is at a 45 degree angle from the straight line, thus the angle of displacement from it must be the angle i got minus the 45 degrees... Thank you!
 
  • #6
The answer is 15.9 degrees west of north. The 61 degrees you get is the total angle.
This means that 45 degrees have to be subtracted from your answer to get to this answer.
Have another look at my drawing to figure this out.
 
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  • #7
andrevdh said:
The answer is 15.9 degrees west of north. The 61 degrees you get is the total angle.
This means that 45 degrees have to be subtracted from your answer to get to this answer.
Have another look at my drawing to figure this out.
yes i looked at it and didnt get it and as soon as i posted my reply i realized what you mean, thanks. Would you mind checking my other two attempts?
 
  • #8
5 also looks fine although I would word it 2.3 degrees north of west.
 

Related to Basic vector addition - my attempts

1. What is vector addition?

Vector addition is a mathematical operation that combines two or more vectors to produce a single vector. It involves adding the magnitudes and directions of the individual vectors to determine the resulting vector.

2. What are the basic rules of vector addition?

The basic rules of vector addition are commutativity, associativity, and distributivity. Commutativity means that the order in which the vectors are added does not affect the result. Associativity means that the grouping of vectors being added together does not affect 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.

3. How do you add vectors graphically?

To add vectors graphically, you must first draw the individual vectors on a coordinate plane. Then, you can use the head-to-tail method or the parallelogram method to determine the resulting vector. The head-to-tail method involves placing the tail of one vector at the head of the other and drawing a line from the tail of the first vector to the head of the second vector. The resulting vector is the line from the tail of the first vector to the head of the second vector. The parallelogram method involves drawing the two vectors as sides of a parallelogram and the resulting vector is the diagonal of the parallelogram.

4. What is the difference between adding vectors algebraically and graphically?

The main difference between adding vectors algebraically and graphically is the method used to determine the resulting vector. Algebraic addition involves breaking down the vectors into their components and adding the corresponding components together to determine the resulting vector. Graphical addition involves visually adding the vectors together using the head-to-tail or parallelogram method.

5. How do you handle vectors in different dimensions when adding them?

When adding vectors in different dimensions, the vectors must first be converted into the same dimension. This can be done by adding zeros to the components of the vector in the lower dimension. Once the vectors are in the same dimension, they can be added using the same methods as adding vectors in the same dimension.

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