Problem of the Week: Suppose a high-powered catapult fires a pumpkin due north with initial speed 80 m/s at an angle of 45 degrees above the horizontal. It is a windy day and so the pumpkin, in flight, undergoes a constant acceleration a = (1,0, -10) (in meters per second squared), where x points east, y points north, and : points up. Find an equation for the pumpkin's position s(t), and use this to figure out when and where it lands relative to its starting point. (Assume the ground is flat and the pumpkin is fired from ground level).