Consider the three displacement vectors A with arrow = ( 2î 3) m, B with arrow =

Question

Consider the three displacement vectors A with arrow = ( 2î 3) m, B with arrow = (7î 7) m, and C with arrow = (7î + 5) m. Use the component method to determine the following. (Take the +x direction to be to the right.)

(b) the magnitude and direction of E with arrow = A with arrow B with arrow + C with arrow magnitude Correct: Your answer is correct. m direction

2.214 points ! Preew:2us Answers SerPSE 10 3 4 PO 17 My Notes Ask Y + Consider the three displacement vectors As ( 3 ) m, B- 71 m, and C (-1+ 5» m use, the component method to determiner he flow ng. Titel e ixdirect on to ete en t (a) the magnitude and direction of the vector D-A++C magnitude 5.385 direction The ange you give does not put the sum ito the correct quadrant. counterdekwise from the +x nxis (b) the magnitude and direction of E- magnitude 19219 direction A B , C 231.34 The ange you give docs not put the sum into the correct quadrant. counterdockwise from the tx axis Need Help?

Explanation / Answer

You have already found magnitude so I'm skipping some steps to find D and E

Part A.

D = A + B + C

D = (-2 i - 3 j) + (7 i - 7 j) + (-7 i + 5 j)

D = -2 i -5 j

|D| = sqrt (2^2 + 5^2) = 5.385 m

Direction = arctan (y/x)

Since D is in 3rd quadrent, So we will add 180 deg to find direction CCW from +x-axis

Direction = 180 deg + arctan (5/2) = 180 deg + 68.2 deg = 248.2 deg

See that we need CCW angle from +ve x-axis

Part B.

E = -A - B + C

E = -(-2 i - 3 j) - (7 i - 7 j) + (-7 i + 5 j)

E = -12 i + 15 j

|D| = sqrt (12^2 + 15^2) = 19.209 m

Direction = arctan (y/x)

Since D is in 2nd quadrent, So we will subtract above angle from 180 deg to find direction CCW from +x-axis

Direction = 180 deg - arctan (15/12) = 180 deg - 51.34 deg = 128.66 deg

See that we need CCW angle from +ve x-axis

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