(5 pts toward any in-class exam) On an alien planet with no atmosphere, acceleration due to gravity is given by g = 12m/s2 . A cannonball is launched from the origin with an initial speed of 90m/s at an angle θ with the horizontal (0 ≤ θ < π/2). (a) Find a function ~r(t) that gives the cannonball’s position after t seconds. Your expression should be in terms of θ. (b) Find the initial angle θ for the cannonball’s velocity that will maximize the horizontal distance the cannonball will travel before hitting the ground. (c) If θ = 30◦ , what is the maximum height of the cannonball? When does it reach that height? In the above, your work should justify your conclusions. You may use the shortcut formulas from section 13.2 to check your answers