A ball is projected vertically from a height of 45 meters with an initial velocity of 40 m/s, and its velocity decreases over time according to the equation v(t) = 40 - 10t. To determine the time it takes for the ball to hit the ground, the height equation h(t) = 45 + 40t - 5t^2 is used. Solving h(t) = 0 leads to the quadratic equation t^2 - 8t - 9 = 0, yielding roots at t = 9 and t = -1. Since negative time is not feasible in this context, the ball hits the ground 9 seconds after being projected. This analysis confirms the relationship between initial velocity, acceleration, and the time of flight for projectiles.