Determine vector components

Solved problems in vectorsdetermine 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)(0.53) = 103 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)(0.53) = 103 Newton (positive because it has same direction with y axis)

F2y = F2 sin 60o = (30)(sin 60o) = (30)(0.53) = -153 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)(0.53) = -23 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)(0.53) = 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)(0.53) = -33 Newton (negative because it has the same direction with -y axis)

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