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Part 1)

Suppose you walk 16.5 m straightwest and then 22 m straight north.   50% Part (a) How far are you, inmeters, from your starting point? 50% Part (b) What is the compass direction, indegrees measured West of North, of a line connecting your startingpoint to your final position? Part 2) A displacement vector points in adirection of θ = 26° left of the positive y-axis.The magnitude of this vector is D = 190 m.   33% Part (a) Enter anexpression for the x-component, Dx, ofthe vector in terms of D and θ.   33% Part (b) Enter an expression forthe y-component, Dy, of the vector interms of D and θ.   33% Part (c) Enter an expressionfor the vector D in unit vector notation in termsof D and θ and the unit vectorsi and j. Part 3) I start walking. The 1stleg of my trip I walk dA = 55 m atθA = 22° south of east. The 2nd legof my trip I walk dB= 55 m atθB = 29° north of east. On my final leg I walkdC = 95 m at θC = 62.5°north of west. Choose the coordinate system so that xisdirected towards the east, and y is directed towards thenorth.   25% Part (a) Write anexpression for the x-component of the final displacementin terms of the given quantities.     25% Part (b) Write an expression forthe y-component of the final displacement in terms of thegiven quantities.   25% Part (c) What is the magnitude ofmy displacement vector (in meters) as measured from theorigin?

Part 4)

Assume that a pilot flies 37 km ina direction 60° north of east and then flies 25 km in a direction15° north of east as shown in the figure.

  50% Part (a) Find herdistance R from the starting point in kilometers.   50%Part (b) Find the angle θ in ° N of E.

Part 5)

Find the following for path C inthe figure, measuring the displacements from the back of the arrow,indicated by a dot, to the arrow’s head. Round to the nearestinteger.

  33% Part (a) Thedistance traveled in meters.   33% Part (b) The magnitude of thedisplacement from start to finish in meters.   33%Part (c) The displacement from start to finish inmeters.