$($iii$)$

The Launch is on the coast and for reasons dictated by the local authorities the launch time cannot coincide with high tide. It is stipulated that the tide must be at least $1$ m below the high tide level for the launch to occur

The tide is level H is given by the equation

$H=15+2\mathrm{.}5**Sin(\frac{2t}{12\mathrm{.}42}+)$

where $H$ is the Height of the tide in metres, $t$ is the time after midnight in hours and $$ is a phase angle $($in radians$)$ for the particular day

On the prospective day of the launch the phase angle is $=\frac{}{6}.$ Calculate

$($a$)$ The level of high tide

$($b$)$ The maximum tidal level allowed during launch

$($c$)$ Furthermore, give the exact time periods in hours and minutes during which launch is allowed.

$($iv$)$ The design team has created a launch support tower which features a number of umbilical connections to the launch vehicle including flexible cables and tubing as well as fully$-$supported solid gantry connections. The launch vehicle will require an electrical support cable under tension to be placed above a fuel delivery gantry by $3$ metres. The ground support design team say that the ideal tension on this cable will give it the equation of $y=3cosh(\frac{x}{6}).$ The umbilical cable ends will be $14$ metres apart. Determine whether this amount of tension on the cable will keep it from interfering with the gantry below.

$($v$)$ A manufacturer has bought some precision made inductors, capacitors and resistors and is looking to produce a component with a total impedance of $8\mathrm{.}000$ and a known but unspecified phase angle.

The components are used to build the following circuit from one non$-$ideal inductor, one capacitor and one resistor. The circuit is designed to be powered by alternating voltage of $50$ Hz