4. (Challenge problem) The acceleration of a projectile on earth at sea level is given as 4 = 0) ay-9 where g 9.81 m/s is the acceleration due to gravity. The subscripts z and y indicate the horizontal and vertical directions, respectively. The sign convention is set so that positive displacements are above and to the right of the origin of our coordinate frame. By hand (.e. using pencil and paper), integrate to find expressions as functions of time for the z-and y-components of velocity and position under these three conditions: a) The projectile is fired in the positive direction at an angle 30 degrees from the horizontal b) The initial position of the projectile is at the origin of the coordinate system c) The initial velocity of the projectile has a magnitude of 5 m/s (3) (4) ile at a given input time t. To test your function create