3. A cannonball is fired with initial speed 100 m/s at an angle of a = 7 (with respect to the horizontal) from a cannon located at the top of a hill 280 meters above ground level. The total acceleration experienced by the cannon ball (including gravity and air resistance) is a(t) = (-t, -10) (where the components are measure in kg. m/s2). (a) Find the cannonball's position vector r(t), t seconds after it is fired. Take the origin O to be at ground level, below the location of the cannon. (b) How many seconds after the cannonball is fired does it hit the ground? (c) Find the horizontal distance traveled by the cannonball before it hits the ground. You can leave your answer in exact form. (d) Suppose instead of reaching the ground, the cannonball hits a wall. Knowing that it hits the wall at a height of 160 meters above ground level, determine the time at which this collision occurs