when does the ball reach its maximum height

Question

a ball is thrown vertically upward in the air, if the ball started from a height of 432 feet off the ground, use the following formula to represent the projection of the ball h=-16t2-24t+432

2. What is the maximum height of the ball? 3. When does the ball return to the ground?

Answer 1

The maximum height occurs at the vertex of the height-vs.-time parabola, which is at

 

t = -24/[2(-16)] sec = ? sec

 

Evaluate h(t) at this value of t to get maximum height.  The ball reaches the ground when 

 

h(t) = 0.

 

Set h(t) equal to zero and solve the resulting quadratic equation for t, using the quadratic formula (which you should know how to apply).  You will get a negative solution and a positive solution.  Discard the negative solution, since time starts at zero.