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d1d1 d2d2 Mr. Bean travels from position 1 (d 1 ) to position 2 (d 2 )

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d1d1 d2d2 d3d3 Mr. Bean then travels from position 2 (d 2 ) to position 3 (d 3 )

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d1d1 d2d2 d3d3 d4d4 Mr. Bean then travels from position 3 (d 3 ) to position 4 (d 4 )

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d1d1 d2d2 d3d3 d4d4 d 1-2 d 2-3 d 3-4 Each change in position is a displacement ( d)

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d 1-2 d 2-3 d 3-4 d initial d final dRdR The overall change in position is the resultant displacement ( d R ) initial position (d initial ) tofinal position (d final )

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d initial d final dRdR d 1-2 d 2-3 d 3-4

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d1 d2 d3 d initial d final d1y d2y d3y d1x d2x d3x To find the resultant displacement algebraically, we need to find the x and y components of each individual vector.

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d initial d final d1y d2y d3y d1x d2x d3x To find the resultant displacement algebraically, we need to find the x and y components of each individual vector. dy dx

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d1y d2y d3y d1x d2x d3x dy dx The next step involves finding the vector sum in the x and y. dx = vector sum of x components dy = vector sum of y components

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dy dx The next step involves redrawing the dx and dy vectors tail to tip.

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dy dx The next step involves redrawing the dx and dy vectors tail to tip.

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dy dx To find the resultant displacement d R draw a new vector from the initial to final position. d initial d final dRdR

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dy dx Use the Pythagorean Theorem to find the magnitude (size) of the resultant. dRdR dR=dR= dy2dy2 dx2dx2 +

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dy dx Use the Pythagorean Theorem to find the magnitude (size) of the resultant and the tangent function to determine the direction of the resultant. dRdR dR=dR= dy2dy2 dx2dx2 + tan = dydy dxdx

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Notice that there are two possible ways of drawing the resultant vector diagram. Each is correct! dRdR dx dy dx dRdR

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Notice that there are two possible ways of drawing the resultant vector diagram. Each is correct! Both the magnitude (size) and direction of the d R remain the same. dRdR dx dy dx dRdR

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Graphical Analytical Component Method

Graphical Analytical Component Method

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