Determine vector components

Solved problems in vectors – determine vector components

1. A force of 20 Newton makes an angle of 30o with the x-axis. Find both the x and y component of the force.

Solving vectors problems – determine vector components 1Solution

Fx = F cos 30o = (20)(cos 30o) = (20)(0.5√3) = 10√3 Newton

Fy = F sin 30o = (20)(sin 30o) = (20)(0.5) = 10 Newton

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2. F1 = 20 Newton makes an angle of 30o with the y axis and F2 = 30 Newton makes an angle of 60o with the -x axis. Find both the x and y components of F1 and F2.

Solving vectors problems – determine vector components 2Solution

F1x = F1 cos 60o = (20)(cos 60o) = (20)(0.5) = -10 Newton (negative because it has same direction with -x axis)

F2x = F2 cos 60o = (30)(cos 60o) = (30)(0.5) = -15 Newton (negative because it has same direction with -x axis)

F1y = F1 sin 60o = (20)(sin 60o) = (20)(0.5√3) = 10√3 Newton (positive because it has same direction with y axis)

F2y = F2 sin 60o = (30)(sin 60o) = (30)(0.5√3) = -15√3 Newton (negative because it has same direction with -y axis)

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3. F1 = 2 N, F2 = 4 N, F3 = 6 N. Find both the x and y components of F1, F2 and F3!

Solving vectors problems – determine vector components 3Solution

F1x = F1 cos 60o = (2)(cos 60o) = (2)(0.5) = 1 Newton (positive because it has the same direction with x axis)

F2x = F2 cos 30o = (4)(cos 30o) = (4)(0.5√3) = -2√3 Newton (negative because it has the same direction with -x axis)

F3x = F3 cos 60o = (6)(cos 60o) = (6)(0.5) = 3 Newton (positive because it has the same direction with x axis)

F1y = F1 sin 60o = (2)(sin 60o) = (2)(0.5√3) = √3 Newton (positive because it has the same direction with y axis)

F2y = F2 sin 30o = (4)(sin 30o) = (4)(0.5) = 2 Newton (positive because it has the same direction with y axis)

F3y = F3 sin 60o = (6)(sin 60o) = (6)(0.5√3) = -3√3 Newton (negative because it has the same direction with -y axis)

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  1. Determine the resultant of in a line vector
  2. Determine vector components
  3. Determine resultant of two vectors using Pythagorean theorem
  4. Determine resultant of two vectors using cosines equation
  5. Determine resultant of two vectors using components of vectors

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