San Francisco is well known for its fog: very thick, low-lying clouds that hide its hills. One foggy day, Penelope is practicing kicking a football. Once she kicks the football so high that it disappears into the fog! The height of the ball (in feet) can be represented at time (in seconds) by the equation h(t)=−16t2+64t . The ball disappears into the fog when it is 40 feet high.

a) Write an inequality that represents the times during which the ball was not visible.

b) Solve the inequality and represent your solution algebraically and on a number line. Also, write a sentence explaining your answer in the context of the problem.

c) How high does Penelope kick the football?

d) When does it reach its maximum height?