Why Does the Book Say the Final Direction is SW When Moving From North to West?

[Kinto]

Problem states that the object is moving North then turns and continues West. The answer on the book says final direction is SW. Shouldn't it be NW?

Thanks.

 

[Pandemonium]

I don't quite get your question, or rather, the question that you're having problems with. Can you please elaborate on it?

 

[Kinto]

The exact wording of the problem in the book is:
A car, moving initially at 32 km/h[N], turns a corner and continues at 32 KM/h[W]. The turn takes 3.0s to complete. Find (a) change in velocity and (b) the average acceleration during the turn.

I got the velocity and the acceleration. But I am having problem with the direction. Since it's going North then it turns west. Shouldn't it be North West? The answer in the book have it as SW.

 

[drag]

Originally posted by Kinto
I got the velocity and the acceleration. But I am having problem with the direction. Since it's going North then it turns west. Shouldn't it be North West? The answer in the book have it as SW.

The value of the velocity did not change, just its
direction. This is an indication of centripatal acceleration.

Live long and prosper.

 

[Hurkyl]

Direction is part of the "value of velocity".


Anyways, how you get the change in velocity and the average acceleration?

 

[Kinto]

I've used the head-to-tail method and got the squared of both velocity to get the resultant. And use the resultant velocity to get the acceleration.

Now trying to picture it. Is it accurate to say direction is southwest because during the turn, the car direction is actually moving southwest from it's original direction of North?

 

[Hurkyl]

Right; the change vector is pointing southwest.

 

[rdecker]

Originally posted by Kinto
I've used the head-to-tail method and got the squared of both velocity to get the resultant. And use the resultant velocity to get the acceleration.

Now trying to picture it. Is it accurate to say direction is southwest because during the turn, the car direction is actually moving southwest from it's original direction of North?

Yes the resultant velocity vector is NW but the change is SW. What textbook are you using?

 

[Kinto]

It's an old textbook. Fundamentals of Physics. I am using the problem there for practice.

 

[HallsofIvy]

In your original post you said "Problem states that the object is moving North then turns and continues West. The answer on the book says final direction is SW. Shouldn't it be NW?"
My reaction was "no, the final directions is West!"

Your error was interpreting "acceleration vector" as "final direction".

Think of it as turning in a circle. Since the speed remains constant the acceleration vector is perpendicular to the line of motion, pointing toward the inside of the circle.