The Water Rocket with length of $2\mathrm{.}85$m$,$ a volume of $6\mathrm{.}77$ L$,$ weight of $1\mathrm{.}55$ kg$.$ Before launching, the rocket is filled with water and pressurized at $640$ psi $(44\mathrm{.}1$ bar$),$ the internal temperature is kept at $37$ degrees Celsius. When launching, the water exits through a nozzle with a diameter of $15\mathrm{.}5$mm$.$ The actual average measured height is $1752$ ft $(534$ m$).$ Using the information provided and by suitable assumptions determine the following:

$($a$)$ The average speed of the exiting water shortly after the rocket leaves the launch pad,

$($b$)$ The absolute temperature of the exiting water, and

$($c$)$ The amount of thrust generated by the water shortly after the rocket leaves the launch pad?

Please state all of your assumptions explicitly and, for any equations you use, please define all variables.