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Question

The two vectors a and b in fig. have equal magnitudes of 10.0m and the angles are θ1=30o and θ2=105o. Find the (a) x and (b) y components of their vectors sum, r, (c) the magnitude of r, and (d) the angle r makes with the positive direction of the x axis
1764732_2951e0ab6e7c4856bdb0a7ab92021600.PNG

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Solution

It should be mentioned that an efficient way to work this vector addition problem is with the cosine law for general triangles (and since a,b and r from an isosecles triangle, the angles are easy to figure). However, in the interest of reinforcing the usual systematic approach to vector addition, we note that the angle b makes with the +x axis is 300+1050=1350

(a) The x component of rx=(10.0m)cos300+(10.0m)cos1350=1.59m

(b) the y component of r is ry=(10.0m)sin1350 = 12.1 m.

(c) the magnitude of r is r = |r|=(1.59m)2+(12.1m)2=12.2m

(d) The angle between r and the +x direction is tan1[(12.1m)/(1.59m)]=82.50

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