You are participating in a navigation exercise as part of earning your pilots li

Question

You are participating in a navigation exercise as part of earning your pilots license. You are instructed to follow the four displacement vectors listed below. Since your fellow flight student has bet you a case of root beer that she will beat you to the landing zone, you decide to plot a direct course from the starting point to final point. (You are completely aware that this is cheating, but you have no scruples when it comes to winning a case of root beer') (All of the directional angles 0, are between and arid are expressed with respect to the cardinal directions.) Derive an expression for the direct course R rightarrow you plotted from the starting. point to the final point. Express your answer in unit-vector notation, in terms of A, B. C, D. theta A, theta C. and theta D Simplify your answer as much as possible. Use the following numerical values and your answer from part (a) to give the magnitude R and direction theta E of your direct course R rightarrow. Use the graph paper provided on the next page to verify your work from parts (a) and (b) Specifically, you should draw vectors A rightarrow through D rightarrow (to scale*) in such a way that you can add them graphically to get vector R. Clearly label your diagram with all relevant symbols and numerical values. Begin at the origin labeled SStart When drawing vectors to scale, you may want to either use a ruler and protractor and/or use the vector components you found in parts (a) and (b) to help you count out squares as needed In either case, use a straight edge to draw your vectors. To fit the diagram on the paper, use the scale . in = , km. FOR FULL CREDIT, show all relevant work and commentary. * All numerical values must include appropriate units, not fast the final answer. Use extra paper if necessary. Staple all of your work together for submission. ('When in doubt, write it out.) You are participating in a navigation exercise as part of earning your pilot's license. You are instructed to follow the four displacement vectors listed below.

Explanation / Answer

a)Let east is positive x direction with unit vector 'i' along it & north is positive y direction with unit vector 'j' along it.

R= A+B+C+D

= [Acos(a) i + Asin(a) j ] + [B j ] + [Csin(c) i - Ccos(c) j ] + [-Dcos(d) i -Dsin(d) j ]

=[Acos(a) + Csin(c) - Dcos(d)] i + [Asin(a) + B - Ccos(c) - Dsin(d) ] j

hence R=[Acos(a) + Csin(c) - Dcos(d)] i + [Asin(a) + B - Ccos(c) - Dsin(d) ] j

So,Rx=[Acos(a) + Csin(c) - Dcos(d)] & Ry= [Asin(a) + B - Ccos(c) - Dsin(d) ]

b)|R|=sqrt(Rx^2 + Ry^2)

=sqrt([Acos(a) + Csin(c) - Dcos(d)]^2 + [Asin(a) + B - Ccos(c) - Dsin(d) ]^2 )

let r is the resultant angle from positive x direction counterclockwise.

r=tan^-1(Ry/Rx)

=tan^-1({Asin(a) + B - Ccos(c) - Dsin(d)}/{Acos(a) + Csin(c) - Dcos(d)})

Hence resultance will make an angle of tan^-1({Asin(a) + B - Ccos(c) - Dsin(d)}/{Acos(a) + Csin(c) - Dcos(d)}) north of east.

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