Vector displacement problem (Physics)

Question

Consider two vectors F~
1 with magnitude 81 N
inclined at 281?
and F~
2 with magnitude 52 N
inclined at 228?
, measured from the positive
x axis with counterclockwise positive.
What is the magnitude of the resultant vector
F~
1 + F~
2 ? Draw the vectors to scale on a
graph to determine the answer.
Answer in units of N. Your answer must
be within ± 5.0%

Answer 1

Hi Sofia!

I am going to leave part of the problem for you to work.

 

Step 1: We break each vector into its x and y components using the trigonometry of sines and cosines.  Make sure to pay attention to the positive and negative signs when doing this.

 

F_1x=F₁[cos(281)]=81N(        )         

F_2x=F₂[cos(228)]=52N(        )

 

F_1y=F₂[sin(281)]=81N(        )

F_2y=F₂[sin(228)]=52N(        )

 

 

Step 2: We add the x-components to get the x component of the resultant vector.

 

R_x=F_1x+F_2x=

 

 

Step 3: We add the y-components to get the y component of the resultant vector.

 

R_y=F_1y+F_2y=

 

 

Step 4: We use the Pythagorean Theorem to compute the magnitude of the resultant from the x and y components of the resultant.

 

R=SQR [Rx²+Ry²]

 

 

Step 5: We find the angle that R makes with the nearest x-axis from tan(theta)=(R_y/R_x), so   theta=arctan(R_y/R_x)