Need Help with a HW problem if anyone would be so kind

[Bryan9129]

Need Help with a HW problem if anyone would be so kind!

Homework Statement

John drives 15 km directly west from Orion to Chester at a speed of 97 km/h, then directly south for 7.0 km to Seiling at a speed of 89 km/h, then finally 33 km southeast to Oakwood at a speed of 90 km/h. Assume he travels at constant velocity during each of the three segments.

(a) What was the change in velocity during this trip? [Hint: Do not assume he starts from rest and stops at the end.]
magnitude ___ km/h
direction ____ ° south of east


(b) What was the average acceleration during this trip?
magnitude ____ km/h2
direction ___ ° south of east

Homework Equations

I honestly don't really know the correct equations. I have tried lots of trig oriented stuff as well as Rx = Ax+Bx+Cx Ry = Ay+By+Cy and R = SQRT (Rx^2 + Ry^2) to find the avg velocity for the trip going from there. Working with three vectors is not something we covered in class at all. I understand that change in velocity is acceleration but I am just not sure how to apply it exactly in this case.

The Attempt at a Solution

I have tried all sorts of ways of setting this problem up and using trig to find the solutions, knowing that the final leg is a 45 degree angle you can create a new triangle with the last leg of the trip as one side, the resultant vector from the firsrt 2 legs of trip as another side, and the hyp would be between the origin and destination. I guess I wrote a lot of my attempts at solutions in section 2, my apologies.

 

[ideasrule]

What was the initial velocity? What was the final velocity? Draw a vector diagram and find the difference between these two vectors.

 

[Bryan9129]

Initial is 97 W, final is 90 SE

You are going to have to forgive me I do not know what the diagram should look like. I have a teacher that instructs by giving a couple of examples rather than the rules that govern the systems as a whole so when I am introduced to a different problem I have to reason my way through it, for some reason I must be thinking about this one in correctly... First thing that comes to mind is to attach the tail of the second vector to the head of the first, but if you breaak the SE vector into its x and y components a right triangle is not created. If you attach the two tails together the result of creating the right triangle of is a hyp of 172.787 km\h which is obviously not appropriate. Hence my issues, I have tried setting up at least 14 different vector diagrams and calculating in different fashions, I must have some fundamental misunderstanding of what I am doing.

The first simple thing I cam up with looks like this :



Sorry for my ignorance in this matter but thanks for the assistance

 

[Bryan9129]

When I use an online vector calc and add 97 @ 180degrees and 90 @ 315 degrees it gives me a resultant of 71.85 @ 242.34 degrees. I have not been able to reproduce that result if it is correct.

 

[jeffity]

I'm with you on this one, Bryan9129. There's an obvious gap in what I've learned at what this problem requires. I'm not even looking for an answer, just a starting point. The simple v-final - v-initial doesn't get me too far.

Sounds like you are using the Giambattista book. The same problem in the end-of-chapter exercises (ch. 3 #43) uses 90 km/h, 80 km/h, and 100 km/h. The answers:

a) 180 km/h @ 24 degrees south of east
b) 280 hm/h^2 @ 24 degrees south of east

I've been trying to arrive at that solution with the book values so I can apply it to my values. While that kind of direction makes sense, I cannot come close to getting any kind of answers applying what I know.

Can anyone offer a little more of a hint on this?

 

[Redbelly98]

Can anyone offer a little more of a hint on this?

I can expand a little on ideasrule's good advice:

What was the initial velocity? What was the final velocity? Draw a vector diagram and find the difference between these two vectors.

You need to use the rules of vector addition & subtraction to figure out what v_f-v_i is. The tip-to-tail method is not very precise. Instead, determine the x and y components of both v_f and -v_i, then add the components.

Do draw a diagram of the two vectors first, as ideasrule said. The figure should show v_f, v_i, and perhaps -v_i as well.

 

[jeffity]

Wow! Took 2 minutes to solve the entire problem! Thank for the tip. Kind of shameful when it comes down to 3rd grade addition, subtraction.

Thanks for not just blurting an answer too. Nobody learns that way.

If you ever want to be TA at my school, I'll put in a good word. Thanks!