Solving Vector Resultants: Magnitude & Direction

[anglum]

vector resultants? please help...

Homework Statement

go 83.9 paces at 188 degrees

turn to 128 degrees and walk 199 paces

then travel 73 paces at 179 degreess

find the magnitude of the resultant displacement from the starting point, answer in units of paces.

and what is the direction of the resultant displacement? use counterclockwise from due east as the positive angular direction between the limits of-180 degrees and +180 degrees. answer in units of degrees.

Homework Equations

The Attempt at a Solution

i have found the x components to be all in teh west direction with the values being
i got these by takin the distance times the cos of the angle
a to b = -83.9
b to c = -122.52
c to d = -72.989

with the resultant being 279.409 west

y components
i got these by taking the distance times the sin of the angle
a to b = -11.68 south
b to c = 156.87 north
c to d = 1.27 north

not sure what the resultant comes to? please help

once i get both resultants correct i use the pythagorean theorem to get the reultant for the distance from a(starting point) to d (ending point) correct?

 

[chaoseverlasting]

Yeah... what youre doing is correct. -11.68 south is equal to 11.68 north. That should help. Do what you did earlier.

 

[m2003]

Dear student,

Thank you for reaching out for help with your problem. It looks like you are on the right track with your calculations for the x and y components. To find the magnitude of the resultant, you can use the Pythagorean theorem as you mentioned. The formula is:

R = √(Rx^2 + Ry^2)

Where R is the magnitude of the resultant, Rx is the x component, and Ry is the y component. Plugging in your values, we get:

R = √((279.409)^2 + (146.45)^2) = 320.58 paces

So the magnitude of the resultant displacement from the starting point is 320.58 paces.

To find the direction of the resultant, we can use the inverse tangent function. The formula is:

θ = tan^-1(Ry/Rx)

Where θ is the direction of the resultant, Rx is the x component, and Ry is the y component. Plugging in your values, we get:

θ = tan^-1(146.45/279.409) = 27.38 degrees

Since the question asks for the direction in units of degrees, we can round to the nearest degree, giving us a direction of 27 degrees counterclockwise from due east.

I hope this helps you with your problem. Good luck with your studies!

Sincerely,