6. 10 points SerPOPS 1.P.045.M My Notes Ask Your A man pushing a mop across a fi

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6. 10 points SerPOPS 1.P.045.M My Notes Ask Your A man pushing a mop across a ficor causes it to undergo two displacements. The first has a magnitude of 152 cm and makes an angle of 128° with the positive x axis. The resultant displacement has a magnitude of 131 cm and is directed at an angle of 36.0 to the positive x axis. Find the magnitude and direction of the second displacement. magnitude direction (counterclockwise from the positive x-axis) Need Help? L. Reede-Lustert Submit Answer Save Progress Practice Another Version 7. -10 points SerPOPS 1.P.062 My Notes Ask Your Express in unit-vector notation the following vectors, each of which has magnitude 42.5 cm (a) Vector E is directed 35.09 counterclockwise from the positive x axis. cm (b) Vector F is directed 35.0° counterclockwise from the positive y axis. cm (c) Vector G is directed 35.0° clockwise from the negative y axis. Need Help?Read lt

Explanation / Answer

the magnitude and direction of the second displacement

B = R-A

Ax = A cos theta = 152 cos 128= -93.58 cm

Ay = A sin theta = 152 sin 128 = 119.77 cm

Rx= R cos theta = 131 cos 36 = 105.98 cm

Ry = R sin theta = 131 sin 36 = 76.99 cm

B = ( Rx-Ax) i + ( Ry - Ay) j

= (105.98-(-93.58) ) i + (76.99-119.77) j

= 199.56 i -42.78 j

magnitude = sqrt ( 199.56)^2 + (-42.78)^2 = 204.09 cm

direction

theta = tan^-1 ( -42.78/199.56) =- 12.09 degree

theta = 360-12.09=347.9 degree

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E = 42.5 (cos35 i + sin35 j)

= 34.81 i + 24.37 j

F = 42.5 (cos125 i + sin125 j) = -24.37 i + 34.81 j

G = 42.5 (cos235 i + sin235 j) = -24.37 i - 34.81 j

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