Basic vector addition - my attempts

[victorhugo]

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

 

[andrevdh]

1. That is correct.
You need to subtract 45^o to get how much to the west of north the direction lies (it helps to make a drawing).

 

[victorhugo]

1. That is correct.
You need to subtract 45^o 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?

 

[andrevdh]

see drawing

 

[victorhugo]

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!

 

[andrevdh]

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.

 

[victorhugo]

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?

 

[andrevdh]

5 also looks fine although I would word it 2.3 degrees north of west.