Answer Happy

Figure 1 shows a car travelling clockwise on a circular track. A camera moves in a guide mounted on
top of the car.
The origin of local co-ordinate system Ω = (ξ, η, ζ) located at the centre of the track. The centre of the
car is R=30 m from the centre of the track (i.e. the bottom of the car is at 𝜌 = [30 0 0]. The car is
travelling at a constant tangential velocity of 21.6 km/hour.
The camera is constrained to move in the ξ-η plane. It moves on a line that makes an angle of 45° to
the horizontal. The guide is mounted at the centre of the roof of the car. The car is h=1.4 m high. (i.e.
the distance from the ground to the mounting point is h).
The distance between the camera and the mounting point on top of the car is governed by the
equation:
𝑆 = 𝑆0 +ℓ𝑠𝑖𝑛 𝛽 𝑡
Where
𝑆0 = 500 𝑚𝑚
ℓ = 300𝑚𝑚
𝛽 = 10𝑟𝑎𝑑/𝑠
𝑡 = 𝑡𝑖𝑚𝑒[𝑠]
Write the expressions for ρ, ρ', ρ'', ω and α which describe the motion of the transducer relative to
the co-ordinate system and the motion of the co-ordinate system itself.
Write an Octave script to calculate the absolute velocity and acceleration of the transducer. The script
must plot the absolute velocity and acceleration against time on separate grids in a single figure
window. The axes must be labelled accordingly. Use a time interval [0,10] s and a time step dt=0.01s.
Use SI units. Your Octave script must perform all the necessary calculations, DO NOT USE A
CALCULATOR.
Submit
• a scan of your mathematics,
• the m files and
• a copy of the graphs. (jpg or pdf - Do not submit a fig file)
Z Y n X