Question

The two vectors and in fig. 3-28 have equal magnitudes of 10.0 m and the angles are 30° and 105°. find the (a) x and (b) y components of their vector sum , (c) the magnitude of , and (d) the angle makes with the positive direction of the x axis.

Answer 1

You can just use basic trigonometry to solve for the x & y components.

vector a = 10cos(30) i + 10sin(30) j = <5sqrt(3), 5>

vector b is only slightly harder because the angle is relative to vector a, and not the positive x-axis. Anyway, this just makes vector b with an angle of 135deg to the positive x-axis.

vector b = 10cos(135) i + 10sin(135) j = <-5sqrt(2), 5sqrt(2)>

So now we can do the questions:

r = a + b

r = <5sqrt(3)-5sqrt(2), 5+5sqrt(2)>

(a) 5sqrt(3)-5sqrt(2)

(b) 5+5sqrt(2)

(c)

|r| = sqrt( (5sqrt(3)-5sqrt(2))2 + (5+5sqrt(2))2 )

= 12.175

(d)

θ = tan-1 ( (5+5sqrt(2)) / (5sqrt(3)-5sqrt(2)) )

θ = 82.5deg