A Lockheed Martin F$-35$ II Lighting jet takes off from an aircraft carrier with a runway length of $90$ m and a takeoff speed $70$ m$/$s at the end of the runway. Jets are catapulted into airspace from the deck of an aircraft carrier with two sources of propulsion: the jet propulsion and the catapult. At the point of leaving the deck of the aircraft carrier, the F$-35$s acceleration decreases to a constant acceleration of $5\mathrm{.}0$m$/$s$25\mathrm{.}0$m$/$s$2$ at $3030$ with respect to the horizontal. $($a$)$ What is the initial acceleration of the F$-35$ on the deck of the aircraft carrier to make it airborne? $($b$)$ Write the position and velocity of the F$-35$ in unit vector notation from the point it leaves the deck of the aircraft carrier. $($c$)$ At what altitude is the fighter $5\mathrm{.}0$ s after it leaves the deck of the aircraft carrier? $($d$)$ What is its velocity and speed at this time? $($e$)$ How far has it traveled horizontally?