Question $3)$

A fighter jet is moving along the shown path with a velocity of $5000\frac{m}{s}$ at angle of ${15}^0$ from the horizontal and an acceleration due to the jet engine in the horizontal direction of $a=6\frac{m}{s^2}.$ At the current altitude the fighter jet has an acceleration due to gravity of $g=9\frac{m}{s}2.$ For the shown instant determine:

a$)$ the radius of curvature of the flight path $($the center of curvature is at $C).$

b$)$ the rate at which the speed $v$ is increasing.