Vector A has a magnitude of 145 units and points 35.0° north of west. Vector B p

Question

Vector A has a magnitude of 145 units and points 35.0° north of west. Vector B points 65.0° east of north. Vector C points 15.0° west of south. These three vectors add to give a resultant vector that is zero. Using components, find the magnitudes of (a) vector B and (b) vector C. The problem is that I do not understand why you add cos of A to sin of B and sin of C. To find x component you would find the cos of B and cos of C to add them all together in order to find the resultant x. Same for resultant of y. The solution manual adds sin of A to cos of B and cos of C to find resultant y. Please explain why you add cos to the sin values and sin to the cos values.

Explanation / Answer

To explain this, draw the x y axes such that positive y direction is north and positive x direction is east. Therefore, negative y direction is South and negative x direction is West.

Now saying that a vector A is 35 degrees North of west means that the angle subtended by Vector A from the negative x axis (West) is 35 degrees. In simple words, "North of West" means that if you go clockwise from West (that is a vector going from west towards North) the angle 35 degrees is when you get your required vector (including its magnitude, ofcourse). And therefore its component in the x direction will be: -145cos35.

Therefore Vector A has angle 35 degrees from the negative x axis.

Similarly, Vector B points 65 degrees east of north. This means that if you go clockwise from North towards East, the angle 65 degrees is when you get the required direction. This means that this angle subtended by vector B is from North (Positive y direction AND NOT x direction which was the case for Vector A). Therefore its x component will be: +Bsin65

Similarly, Vector C points 15 degrees west of south. This means that if you go clockwise from South direction towards West then the angle 15 degrees is the required angle for the vector. And so the angle subtended by vector C is from South (negative y direction AND NOT x direction). Therefore its x component will be: -Csin15

Get two equations for x components and y components and equate it to zero (since the resultant is zero in both x and y direction).

Solve the two equations simultaneously to get B and C.

Related Questions

Navigate

• Browse (All)
• Browse V
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.