Vector-Displacement

[Temperature101]

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This seems to be an easy problem but I am having a hard time figuring it out...

Calculate your displacement after walking 3 mi north, then 6 mi west, then 5 mi north.
A. 6
B. 8
C. 10
D. 14

Answer: C

 

[Jepstein30]

This seems to be an easy problem but I am having a hard time figuring it out...

Calculate your displacement after walking 3 mi north, then 6 mi west, then 5 mi north.
A. 6
B. 8
C. 10
D. 14

Answer: C

Same as walking 8 north and 6 west. Pythagorean theorem problem.

8^2 + 6^2 = x^2
64+36 = 100 = x^2
x= 10

 

[Temperature101]

Same as walking 8 north and 6 west. Pythagorean theorem problem.

8^2 + 6^2 = x^2
64+36 = 100 = x^2
x= 10

I understand the math. My problem is how do they add these vectors. I though that we have to find the resultant vector for the first two vectors and then conbine it with 6 miles west and find the displacement. This clearly wont be a right triangle.

 

[Raiden2012]

It might help if you just consider starting and end points. After all, it is displacement. Not sure if it helps

 

[Jepstein30]

I understand the math. My problem is how do they add these vectors. I though that we have to find the resultant vector for the first two vectors and then conbine it with 6 miles west and find the displacement. This clearly wont be a right triangle.

So we have 3 vectors:

3 mi north
6 mi west
5 mi north

We can add these in any order, like typical addition.

So we'll add 3 mi north and 5 mi north first = 8 mi north.

Now, 8 mi north + 6 mi north. Tail to head vector addition makes a right triangle.

 

[Temperature101]

So we have 3 vectors:

3 mi north
6 mi west
5 mi north

We can add these in any order, like typical addition.

So we'll add 3 mi north and 5 mi north first = 8 mi north.

Now, 8 mi north + 6 mi north. Tail to head vector addition makes a right triangle.

You meant 8 mi north + 6 mi west? I thought these vectors must be added in the order given...Clearly I was wrong. Unbelievable I would have missed something elementary like that if it was in the mcat.

 

[Jepstein30]

You meant 8 mi north + 6 mi west? I thought these vectors must be added in the order given...Clearly I was wrong. Unbelievable I would have missed something elementary like that if it was in the mcat.

yah 6 west.

It's just like normal addition.. you can add in any order.

Because think about it. Whether you go 8 miles north and then 6 west you end up at the same spot as the 5 north, 6 west, 3 north path.