Consider two vectors F?1 and F?2 with magnitude F1=64N and F2=71N and where ?1 =

Question

Consider two vectors F?1 and F?2 with magnitude

F1=64N and F2=71N

and where ?1 = 251 degrees and ?2 = 107 degrees. The angles are measured from the positive x axis with the counter-clockwise angular direction as positive.

a) What is the magnitude of the resultant vector F, where F=F1+F2? Answer in units of N.

b) What is the direction of this resultant vector F?? Use counterclockwise as the positive angular direction, between the limits of -180 degrees and +180 degrees as measured from the positive x axis. Answer in units of degrees.

Explanation / Answer

add components

x = 64*cos(251 degrees) + 71*cos(107 degrees)= -41.58 N

y = 64*sin(251 degrees) + 71*sin(107 degrees)=7.38 N

mag = sqrt(41.58^2 + 7.38^2)= 42.23 N

direction = arctan(y/x) = arctan(7.38/-41.58)= 170 degrees

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