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 242 km and a direction 30.0 degrees north of east. The displacement vector B for the second segment has a magnitude of 173 km and a direction due west. The resultant displacement vector is R = A + B and makes an angle ? with the direction due east. Using the component method, find (a) the magnitude of R and (b) the directional angle ?. Answer must be in 4 significant figures.

Explanation / Answer

component of vector A due east=242cos30 km = 209.57 km

component of vector A due north=242sin30 km = 121 km

vector B is 173 km due west,

So net component of resultant vector R is 121 km due north and(209.57-173)=36.57km due east

magnitude of R =((121)^2+(36.57)^2)= 126.4 km

let it makes angle with east

126.4cos=36.57

=>=73.2o with east

a) magnitude of R = 126.4km

b)73.2o with east

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