A pilot flies her route in two straight-line segments. The displacement vector A

Question

A pilot flies her route in two straight-line segments. The displacement vector A for the first segment has a magnitude of 255 km and a direction 30.0 degree north of east. The displacement vector for the second segment has a magnitude of 164 km and a direction due west. The resultant displacement vector is R = A + B and makes an angle theta with the direction due east. (a) Using the component method, find the magnitude of R. R= km (b) Using the component method, find the directional angle theta. theta = degree

Explanation / Answer

Breaking down into components,

Ax = Acos30 = 220.84 km
Ay = Asin30 = 127.5 km

Bx = -164 km
By = 0 km

Adding components,

Rx = 56.8364 km
Ry = 127.5 km

Getting the resultant,

R = 129.59 km [ANSWER, A]
theta = 65.974 degrees [ANSWER, B]

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