Please help me answer this question, I\'m a bit lost. Thank you; will rate answe

Question

Please help me answer this question, I'm a bit lost. Thank you; will rate answer.

1. Find the magnitude and direction of the sector C that is the sum of the vectors B B and shown in the sketch, C A 2B. Vector A has magnitude 5.0 m and is in the +x direction. vector B has magnitude 8.0 m and is in the 4' quadrant and makes an angle of 37o with the y axis. a. Specify the direction of c by giving the angle that it makes with the +x axis, with counterclockwise angles being positive. Ans. b. Perform vector addition graphically and show the resultant vector C on the graph below. 2. Find the magnitude and direction of the vector D that is the difference of the vectors and B, i.e. D A- B. Vectors A and Bremain the same as for the first problem. a. Specify the direction of D by giving the angle 0 that it makes with the +x axis, with counterclockwise angles being positive.) IDI Ans. b. Perform vector addition graphically and show the resultant vector D on the graph below.

Explanation / Answer

Given that

vector B=8 cos(360-37) i+8sin(360-37) j=6.4 i-4.8 j

vector A=5 i

now we find the vector C

vector C=A+2B=5i+2(6.4i-4.8j)

=17.8 i-9.6 j

the magnitude vector C=[17.8^2+9.6^2]^1/2=20.2 m

direction =tan^-1[-9.6/17.8]=331.7 degree

..................................................................................................................................................

2 problem

the vector D=A-B

=(5i)-(6.4i-4.8j)

=-1.4i+4.8 j

magnitude of vector D=[1.4^2+4.8^2]^1/2=5 m

direction =tan^-1[-4.8/1.4]=286.3 degree

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