For the vectors given in Fig. 3-32 (|A| = 65.0 and θ = 50.0°), determine the following.?
http://www.webassign.net/giancoli5/3_35alt.gif
Figure 3-32
(a) A - B + C
Magnitude
Direction
(b) A + B - C
Magnitude
Direction
(c) C - A - B
Magnitude
Direction
I already know the answers. But I just need to know how to do these. I solved for each side by using the resultant times the cos or sin of the angle.
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The video-lesson in the link explains the method. I'll do the 1st one though.
Make sure you get the signs of each component correct.
x-component of A = 65.0cos(28.0°) = 57.39
y-component of A = 65.0sin(28.0°) = 30.52
x-component of B = -40cos(50.0°) = -25.71
y-component of B = 40sin(50.0°) = 30.64
x-component of C = 0
y-component of C = -46.8
We want A - B + C. Check the following 3 lines carefully:
Total x-component = (x-component of A) - (x-component of B) + (x-component of C)
= (57.39) - (-25.71) + (0)
= 83.1
Similarly, total y-component = (30.52) - (30.64 + (-46.8) = -46.92
Resultant, R, is given by R² = 83.1² +(-46.92)²
R = √9107 = 95.4
From a suitable diagram of the total x and y components, you see the resultant makes an angle θ clockwise from the +x axis given by:
tanθ = 46.92 / 83.1
θ = tan⁻¹ 0.5646 = 29.4°
(Though my arithmetic isn't' guaranteed)
The others are done the same way.