A remote-controlled drone travels along a straight vertical path

MATHEMATICS · Multi-part · AP · AP Precalculus · Trigonometric and Polar Functions · Trigonometric and Polar Functions

Problem

A remote-controlled drone travels along a straight vertical path. For 0≤t≤90\le t\le 9 seconds, its velocity (in m s−1\text{m}\,\text{s}^{-1}) is modeled by v(t)=4cos⁡ ⁣(πt3)−1.v(t)=4\cos\!\left(\frac{\pi t}{3}\right)-1. Answer the following questions about the motion. (1) Part 1: (a) Solve v(t)=0v(t)=0 for tt in the interval 0≤t≤90\le t\le 9. Express exact values of tt. (2) Part 2: (b) Construct a sign chart for v(t)v(t) on [0,9][0,9] and use it to state the open sub-intervals on which the drone ascends and the sub-intervals on which it descends. (3) Part 3: (c) At each rest time identified in part (a), determine whether the drone changes direction. Justify your conclusion.

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