What is the direction of the resultant displacement from the starting point?

[delfam]

Vector Help, Finding Angle

Homework Statement

Instructions for finding a buried treasure include the following: Go 114.6 paces at 285◦,
turn to 247◦ and walk 112 paces, then travel 399 paces at 284◦. Find the magnitude of the resultant displacement from the starting point.
Answer in units of paces.

What is the direction of the resultant displacement? Use counterclockwise from due East as
the positive angular direction, between the limits of −180◦ and +180◦.
Answer in units of ◦.

Homework Equations

arctan(Cy/Cx) = theta c

The Attempt at a Solution

I did the first part of the problem and got 605.98 paces which I know is correct. So to find the angle in part b i use arctan(Cy/Cx).

arctan(-600.37/82.28) = -82.2, then absolute value it
360 - 82.2 = 277.8 degrees.

Im not sure what I'm doing wrong, I know Cy(-600.37) and Cx(82.28) are right as I got part 1 right. I am having trouble with the wording of part b cause I can't get the right angle.

 

[berkeman]

Homework Statement

Instructions for finding a buried treasure include the following: Go 114.6 paces at 285◦,
turn to 247◦ and walk 112 paces, then travel 399 paces at 284◦. Find the magnitude of the resultant displacement from the starting point.
Answer in units of paces.

What is the direction of the resultant displacement? Use counterclockwise from due East as
the positive angular direction, between the limits of −180◦ and +180◦.
Answer in units of ◦.

Homework Equations

arctan(Cy/Cx) = theta c

The Attempt at a Solution

I did the first part of the problem and got 605.98 paces which I know is correct. So to find the angle in part b i use arctan(Cy/Cx).

arctan(-600.37/82.28) = -82.2, then absolute value it
360 - 82.2 = 277.8 degrees.

Im not sure what I'm doing wrong, I know Cy(-600.37) and Cx(82.28) are right as I got part 1 right. I am having trouble with the wording of part b cause I can't get the right angle.

Could you please list the delta-x and delta-y components of each of the three displacement vectors that you are given? It would help us to check your work if we had each of the 3 displacement vectors in rectangular notation, so we can check the sum.

 

[delfam]

Ax = 114.6cos(285) = 29.51
Bx = 112cos(247) = -43.76
Cx = 399cos(284) = 96.53
Dx = 29.51 = (-43.76) + 96.53 = 82.28

Ay = 114sin(285) = -110.12
By = 112sin(247) = -103.10
Cy = 399sin(284) = -387.15
Dy = -110.12 + (-103.10) + (-387.15) = -600.37

(82.28)^2 + (-600.37)^2 = 367214.14, square root of 367214.14 = 605.98
so the displacement is 605.98, but now I need the angle so

arctan(-600.37/82.28) = -82.2 then take absolute value of that and
360 - 82.2 = 277.8 degrees.

But 277.8 isn't right cause I got it wrong, but I'm not sure where I went wrong cause I know I got the displacement right, the wording of part 2 is really weird so that's maybe were I messed up.

 

[zgozvrm]

Re-read the original question. You misread one of the numbers.

 

[delfam]

what, the 114.6, that was just a typo, I still don't understand the second part. "What is the direction of the resultant displacement? Use counterclockwise from due East as
the positive angular direction, between the limits of −180◦ and +180◦.
Answer in units of ◦."

I just don't get the wording

 

[berkeman]

what, the 114.6, that was just a typo, I still don't understand the second part. "What is the direction of the resultant displacement? Use counterclockwise from due East as
the positive angular direction, between the limits of −180◦ and +180◦.
Answer in units of ◦."

I just don't get the wording

You found:

arctan(-600.37/82.28) = -82.2

That -82.2 degrees is the angle down from the positive x-axis to the final vector. And the problem wants you to express the answer as measured from "East" (the positive x axis) to the vector, bounded by +/-180 degrees. Since the vector resultant is in the lower right quadrant, and you measure down to it from the x axis, what is the answer for the final direction?

 

[delfam]

You found:



That -82.2 degrees is the angle down from the positive x-axis to the final vector. And the problem wants you to express the answer as measured from "East" (the positive x axis) to the vector, bounded by +/-180 degrees. Since the vector resultant is in the lower right quadrant, and you measure down to it from the x axis, what is the answer for the final direction?

-82.2, thanks for the help.