TBR Physics question

[helix]

Hi All,
Here's the question -
In map making, cartographers sometimes rely in measurements taken by a surveyor. A person reports that she walked 3200m north and then 2400m west before reaching the measurement site. What is the magnitude and direction of the shortest path between her starting and ending points?
A. 4000m 37' west of North
B. 4000m 53' west of North
C. 5600m 37' west of North
D. 5600m 53' west of North

I figured out the 3-4-5 angle and still could not get the correct answer. Could someone please explain?

Thanks and sorry if this is a repeat...could not find it anywhere in the thread.

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[Geekchick921]

Moving this to the Study Questions Q&A sub-board, by the way!

Well, if you got the 3-4-5 part down you know the distance is 4000m. Beyond that it's pretty easy, if you consider the length of the side opposite the angle, and/or if you drew a diagram at least somewhat to scale, you should be able to tell if the angle is less than 45 degrees or greater than 45 degrees.

Remember, they're asking you to base the angle from the north line/Y-axis, not the X-axis.

 

[BerkReviewTeach]

Hi All,
Here's the question -
In map making, cartographers sometimes rely in measurements taken by a surveyor. A person reports that she walked 3200m north and then 2400m west before reaching the measurement site. What is the magnitude and direction of the shortest path between her starting and ending points?
A. 4000m 37' west of North
B. 4000m 53' west of North
C. 5600m 37' west of North
D. 5600m 53' west of North

I figured out the 3-4-5 angle and still could not get the correct answer. Could someone please explain?

Thanks and sorry if this is a repeat...could not find it anywhere in the thread.

For the 3-4-5 right triangle method, you'd first need to divide by 800 to get the values. 2400/800 = 3 and 3200/800 = 4, so 3-4-5 is actually (3 x 800)-(4 x 800)-(5 x 800). 5 x 800 = 4000, so that gives you the magnitude. Even with that, you could have actually found it by elimination, because the resultant vector has to be less than 5600 (the scalar sum of 2400 and 3200). This eliminated choices C and D. from there, you just need to visualize (or draw) the vector to see if it favored west or north. Because she's walked more north than west, the vector will be a small angle from north in the west direction.

I've atatched the solution from the book.

View attachment 14427

 

[helix]

Thanks! I wasn't able to determine the the angle in the figure...but I got it now!