Finding Displacement with angles and directions

[Shanetm]

Homework Statement

I am having a nightmare doing homework for my physics test. I have figured out part of the answer but can not figure out what the angle of the displacement is and its driving me crazy...

The teacher showed us two methods of how to find the answers, but ended up making an error somehow on the first example which was never resolved, which is the one I am going by making it that much harder since I prefer that method(The other method is the one that you have to find Δd1x and Δd2x then Δd1y and Δd2y and go from there) It seems much simpler and he got the right answer using it vs the method mentioned earlier, but when I tried it the answer I got was even more far off so I clearly don't know where I am going with it. (maybe if someone is able to explain it to me, it would be more effective)

The question I can't figure out is "A dog runs after a ball 24m [W 12° S] and then heads 33m [E 52° S] after being distracted by a squirrel. What is his displacement?

Homework Equations

Δd1=24 [W12°S]
Δd2=33 [E52°S]
ΔdT=?

The Attempt at a Solution

I have drawn the triangle, and labelled its sides, decided the two distances create a 64° angle and so far have managed to find out the displacement is 31 meters by using the formula c^2=a^2+b^2-2abCOSc. My problem is figuring out the correct formula to obtain the angle. I've tried different methods and none of them work. The answer is supposed to be 31m[W84°S] this textbook has been wrong multiple times in the past however. Any help is appreciated as the test is tomorrow and I'm sure this will be on it.

 

[PeterO]

Homework Statement

I am having a nightmare doing homework for my physics test. I have figured out part of the answer but can not figure out what the angle of the displacement is and its driving me crazy...

The teacher showed us two methods of how to find the answers, but ended up making an error somehow on the first example which was never resolved, which is the one I am going by making it that much harder since I prefer that method(The other method is the one that you have to find Δd1x and Δd2x then Δd1y and Δd2y and go from there) It seems much simpler and he got the right answer using it vs the method mentioned earlier, but when I tried it the answer I got was even more far off so I clearly don't know where I am going with it. (maybe if someone is able to explain it to me, it would be more effective)

The question I can't figure out is "A dog runs after a ball 24m [W 12° S] and then heads 33m [E 52° S] after being distracted by a squirrel. What is his displacement?

Homework Equations

Δd1=24 [W12°S]
Δd2=33 [E52°S]
ΔdT=?

The Attempt at a Solution

I have drawn the triangle, and labelled its sides, decided the two distances create a 64° angle and so far have managed to find out the displacement is 31 meters by using the formula c^2=a^2+b^2-2abCOSc. My problem is figuring out the correct formula to obtain the angle. I've tried different methods and none of them work. The answer is supposed to be 31m[W84°S] this textbook has been wrong multiple times in the past however. Any help is appreciated as the test is tomorrow and I'm sure this will be on it.

Now that you have all three sides of the triangle, you can use sine rule or cosine rule to find the other angles in the triangle.

You may find that the angle between this resultant displacement and the W12S displacement is , say, 70^o.

That means the resultant is 70^o more than West 12^o S, which would make it W 82^o S

If the answer really is W 84^o S, then that angle in the triangle must actually be 72^o.

 

[Shanetm]

Okay, I think I understand now. Since the angles I have to work with are 72° and 12° (d1), the answer would be 84°

I think that sheds a bit of light on things. Thank you Peter. I will definitely make sure I keep this in mind

Edit: I've run into a bit of an issue. I've been using the SIN law and doing the calculation 33SIN64 (Divided by 31) to find the resultant angle and I keep getting 73 and not 72... Arghh

However, If I find 24SIN64 (Divided by 31), I get 44 and then add 33 to it which becomes 84

Im so confused right now )=

Edit again: Okay, I figured this out for good! What I was doing wrong was not leaving the extra decimal places in the equation when dividing my 31. All I had to do was divide by 33.16 which was the answer from before and bang, got my answer. Woot!

-Shane