Question 3. (4 points for each part (a)-(b), graded for correctness) Consider an airplane on the runway preparing for takeoff. (13) Suppose the engine dies at the moment the plane leaves the runway at an angle of 6' = g with the horizontal (hence the velocity makes angle 9 with the horizontal). What is the maximum height the airplane reaches before starting to fall? HINT: The vertical component of the plane's velocity is v(t) = 119 - gt and its height is h(t) = vat - gtz, where no = 180 sin(0) and g = 10 m/52 is the acceleration due to gravity near the surface of the Earth