? Figure 1: The motion of an elevator [E] in a mine-shaft. The top of the shaft is denoted by the position I : 0. such that :1" increases in the downwards direction. That is. positive values of :r denote the depth of the elevator in the mine-shaft. (3) Identify the following features of the function eq. [2}: . Amplitude - l'eriod . Phase shift . Vertical shift. [5] (b) If the elevator travels up and down the entire depth, how deep is the mine-shaft? [1] (c) Plot the function eq. (2) over the domain t = 0 to f = 400x. Hint: It might help to identify the 'five key points'. [4] (d) Suppose that the speed of the elevator at any time is given by v(t) = sin Too (3) What is the speed of the elevator when it reaches its maximum depth? Explain what this means for the motion of the elevator. [3]