Question 10 The graph in Figure 3 represents a displacement map used to control the altitude, , of a drone over an interval of 25 seconds. 15l Figure 3 The vertical displacement of a drone with respect to time (a) Find the following: (i) the time at which the altitude is a maximum (i} the times at which the velocity is zero (iii) the approximate time at which the velocity is a positive maximum and the magnitude of the velacity at that time. (8 marks) {b) Draw a graph of the vehicle's intended velocity with respect to time over the interval 0 to 25 seconds. Absolute precision is not required, however, your graph should be approximately correct with respect to time and velocity, in particular, at the points where the velocity is an extremum. {10 marks) A sensor is attached to the rim of a vehicle's wheel to measure displacement in relation to a fixed point on the ground. The curve that describes the displacement of the sensor with respect to a fixed point is given by the functions: *(1) = 4ecos(wt) and w(t) = =5t + 4 sin{wt) where w is measured in rad . (c) Given that the velocity can be expressed as a vector in the form: de, d V= El + d_}tl and the acceleration as a vector in the form: 2 2 a= :T':I + iT{I find vector expressions for: (i) the sensor's velocity vector (i) the sensor's acceleration vector (iii) the magnitude of the acceleration in terms of w