Part 1) Suppose you walk 16.5 m straight west and then 22 m straight north. 50%...

Part 1)

Suppose you walk 16.5 m straight west and then 22 m straight north.

50% Part (a) How far are you, in meters, from your starting point?

50% Part (b) What is the compass direction, in degrees measured West of North, of a line connecting your starting point to your final position?

Part 2)

A displacement vector points in a direction of θ = 26° left of the positive y-axis. The magnitude of this vector is D = 190 m.

33% Part (a) Enter an expression for the x-component, D_x, of the vector in terms of D and θ.
33% Part (b) Enter an expression for the y-component, D_y, of the vector in terms of D and θ.

33% Part (c) Enter an expression for the vector D in unit vector notation in terms of D and θ and the unit vectors i and j.

Part 3)

I start walking. The 1^st leg of my trip I walk d_A = 55 m at θ_A = 22° south of east. The 2^nd leg of my trip I walk d_B= 55 m at θ_B = 29° north of east. On my final leg I walk d_C = 95 m at θ_C = 62.5° north of west. Choose the coordinate system so that xis directed towards the east, and y is directed towards the north.

  25% Part (a) Write an expression for the x-component of the final displacement in terms of the given quantities.
  25% Part (b) Write an expression for the y-component of the final displacement in terms of the given quantities.
  25% Part (c) What is the magnitude of my displacement vector (in meters) as measured from the origin?

Part 4)

Assume that a pilot flies 37 km in a direction 60° north of east and then flies 25 km in a direction 15° north of east as shown in the figure.

50% Part (a) Find her distance 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 in the figure, measuring the displacements from the back of the arrow, indicated by a dot, to the arrow’s head. Round to the nearest integer.

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

Solutions

Expert Solution

genius_generous answered 1 year ago

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