Question

A. Given two vectors ~F1, and ~F2. Where the magnitude of these vectors are F1= 81 N, and F2= 90 N. And where θ1= 80◦,and θ2= 22◦. The angles are measure from the positive x axis with the counterclockwise angular direction as positive. What is the magnitude of the resultant vector ||~F||, where ~F= ~F1+ ~F2?
Answer in units of N.


B. Note: Give the angle in degrees, use counterclockwise as the positive angular direction,
between the limits of −180◦and +180◦from the positive x axis.
What is the direction of this resultant vector ~F?
Answer in units of◦.

Answer 1

A. F = F1 + F2 = 81N[80o] + 90N[22o]

F=(81*cos80+90*cos22)+(81*sin80+90*sin
22)i = 97.51 + 113.5i
F = sqrt(97.51^+113.5^2) = 149.6 N.

B. Tan A = Y/X = 113.5/97.51 = 1.16398
A = 49.3o = Direction.