Chapter 03, Problem 065 A protester carries his sign of protest, starting from t

Question

Chapter 03, Problem 065 A protester carries his sign of protest, starting from the origin of an xyz coordinate system, with the xy plane horizontal. He moves 35 m in the negative direction of the x axis, then 20 m along a perpendicular path to his left, and then 32 m up a water tower. In unit-vector notation, what is the displacement of the sign from start to end? (a), (b) and (c) for x, y and z components respectively) (d) The sign then falls to the foot of the tower. What is the magnitude of the displacement of the sign from start to this new end? (a) Number (b) Number (c) Number (d) Number Units Units Units Units

Explanation / Answer

Orient the y-axis at 90 CCW from the x-axis (normally), and make +z vertically upward.

a), b), c)

The three displacements are (35 i^ m), (20 j^ m), and (+32 k^ m).

Adding these: r = (35 i^ 20 j^ + 32 k^) m.

d) The new displacement of the sign is now

rf, sign = (35 i^ 20 j^) m

Its magnitude is by Pythagoras:

|rf, sign| = sqrt[35^2 + 20^2] = 40.3 m

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