$3-)$ An airplane, while flying, is subjected to air resistance that is proportional to square of its velocity. There is another resistive force on the airplane caused by the air flow over the wings. Air flowing over the wings is pushed down and slightly forward, so from Newton's third law the air exerts a force on the wings and airplane that is up and slightly backward. The upward force is the lift force that keeps the airplane aloft, and the backward force is called induced drag. At flying speeds, induced drag is inversely proportional to $v^2,$ so that the total air resistance force can be expressed by $F_{\text{a}\text{i}\text{r}}=v^2+\frac{}{v^2},$ where $$ and $$ are positive constants that depend on the shape and size of the airplane and the density of the air. If $=0\mathrm{.}3N\frac{s^2}{m^2},=3\mathrm{.}5{10}^{5}N\frac{s^2}{m^2}$ for an airplane that is flying from Ankara to Istanbul. In a steady flight, the engine must provide a forward force that exactly balances the air resistance force.

a$-)$ Calculate the speed at which this airplane will have the maximum range for a given quantity of fuel

b$-)$ Calculate the speed for which the airplane will have the maximum endurance $($that is$,$ remain in the air the longest time$)$