A drone begins at ground level directly above the origin of a three-dimensional…

PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Kinematics · Kinematics

Problem

A drone begins at ground level directly above the origin of a three-dimensional coordinate system. The drone then executes the following flight plan: • Leg 1: It travels

200\,\text{m}

in a straight line at a constant speed, heading

40^{\circ}

north of east in the horizontal plane, and rising uniformly to an altitude of

30\,\text{m}

over a time interval of

120\,\text{s}

. • Leg 2: Without pausing, it next flies for

90\,\text{s}

along a straight line that carries it

150\,\text{m}

due east while climbing uniformly to a final altitude of

80\,\text{m}

. Assume each leg is completed at constant velocity (both magnitude and direction). (a) Determine the

x

y

-, and

z

-components of the drone’s displacement for each leg. (b) Compute the drone’s total displacement vector from the origin, expressing your answer in component form. (c) Calculate the magnitude and the bearing (angle measured east of north in the horizontal plane) of the drone’s average velocity vector for the entire flight. Also state the average vertical component of velocity. (d) Suppose Leg 2 required

120\,\text{s}

instead of

90\,\text{s}

while covering the same spatial displacement. Qualitatively describe how this change would affect the magnitude of the average velocity for the entire flight and justify your reasoning.

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