The vector A has a magnitude of 5 mph and points along the x-axis, vector B has
ID: 2185074 • Letter: T
Question
The vector A has a magnitude of 5 mph and points along the x-axis, vector B has a magnitude of 8 mph and makes an angle of 150 degrees, and vector C has a magnitude of 10 mph and an angle of 255 degrees. Please draw the vectors on paper and complete the sections (a), (b), and (c). Note the unit mph stands for miles per hour. Explain the scale in your drawing and label lengths and angles.(a) Find the total vector, T= A + B +C , graphically by tracing the arrows in your notebook and drawing the total vector. Measure the magnitude and direction of the total vector using your ruler and protractor. r B r C
(
b) Then, perform the addition mathematically in terms of the magnitudes and directions of the components.
(c) Is the graphical total vector consistent with the calculated T ?
Explanation / Answer
Let us the Component Method to get the resultant vector T. A = 5 mph along the x-axis Ax = + 5 mph Ay = 0 mph B = 8 mph at an angle of 150 Bx = 8cos150 = - 6.93 mph By = 8sin150 = 4 mph C = 10 mph at an angle of 255 Cx = 10cos255 = - 2.59 mph Cy = 10sin255 = - 9.66 mph Rx = Ax + Bx + Cx Rx = 5 + -6.93 + -2.59 Rx = - 4.52 Ry = Ay + By + Cy Ry = 0 + 4 + - 9.66 Ry = - 5.66 T = sqrt[Rx^2 + Ry^2] T = sqrt[(-4.52)^2 + (- 5.66)^2] T = 7.24 mph Let ? = the angle formed by T with the x-axis. We know ? is in the 3rd quadrant because Rx is negative and Ry is negative. ? = arctan(Ry/Rx) ? = arctan(5.66/4.52) ? = 51.39 degrees, below the negative x-axis ANSWER: T = 7.24 mph, 51.39 deg south of west
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