Pythagorean theorem and vectors

[jai6638]

The summit of a mountain, 2450 m above base camp, is measured on a map to be 4580 m horizonttally from the camp in a direction 32.4 degrees west of north. What are the components of the displacement vector from camp to summit? What is its magnitude? Choose the x-axis east, y-axis north and z axis up.

I made a right triangle with 2450 on the y-axis and 4580 on the x-axis with a theta of ( 90-32.4= 57.6 degrees) and use pythagorean theorm to find the resultant. However, the answer at the back of the book is different from mine..

Any ideas what am I doing wrong?

THanks

 

[Leong]

i think 2450 m is for the z axis. to find the x and y components you will have to use 4580 and the angle given.

 

[jai6638]

your right... it corresponds with textbook answer.. but why is it the Z axis? and not a right triangle with the two sides being 4580 and 2450?

thanks

 

[jai6638]

it says that the components are -2450 , 3867 and 2450... Why is the first 2450 a negative?

Would it be possible for you to tell me what the diagram would look like? i'd really appreciate it.

thanks much.

 

[HallsofIvy]

A standard map has north upward, east to the right. A standard graph has positive y upward, positive x to the right.

That is, east is positive x, west is negative x.

You are welcome to set up your coordinates anyway you want but if they are not standard, you'd better say so!

 

[BobG]

it says that the components are -2450 , 3867 and 2450... Why is the first 2450 a negative?

Would it be possible for you to tell me what the diagram would look like? i'd really appreciate it.

thanks much.

What are the components of the displacement vector from camp to summit? What is its magnitude?

From camp to summit would have a negative x (North is 90 deg counterclockwise of East, plus the 32.4 degrees West of North), positive y (either sine of 122.4 or cosine of 32.4, depending on whether you want to change your reference or not), and a positive z.

Normally, the vector would be given with the x coordinate first, the y second, and the z third. Look at the similarity between your first coordinate and third coordinate (actually, the x is closer to -2454, which would be more in line with the significant digits used for the y).

For the magnitude, just use the Pythagorean Theorem (it works just as well in three dimensions as in two dimensions - in fact it works in any number of dimensions)

 

[HallsofIvy]

And, of course, the problem asked for the displacement vector, not just for the straight line distance between the two points!