Question

The two vectors\(\vec{a}\) and \(\vec{b}\) in the figure have equal magnitude of 26 m and the angles are θ1=28° and θ2 = 103°. Find the x-component of their vector sum r.

Find the y-component of their vector sum r.

What is the magnitude of their vector sum r?

Find the angle that their vector sum r makes with the positive direction of the x-axis.  

Answer 1

given that : |a| = magnitude of "a" = |b| = magnitude of "b" = 34 m

= (|a| Cos) i + (|a| Sin) j = (34 Cos28) i + (34 Sin28) j = 30.02 i + 15.96 j

= (|b| Cos) i + (|b| Sin) j = (34 Cos(28 + 103) i + (34 Sin(28 + 103)) j = - 22.31 i + 25.66 j

Sum is given as

=+

= (30.02 i + 15.96 j ) + (- 22.31 i + 25.66 j )

= 7.71 i + 41.62 j

hence the x-component of the sum = 7.71 m

the y-component of the sum = 41.62 m

magnitude : || = sqrt((7.71)² + (41.62)²) = 42.33 m

direction : = tan^-1(41.62/7.71) = 79.5 deg counterclockwise from positive x-axis