Final answer:
To determine when the ball reaches the ground, we need to set the height equation equal to zero and solve for time using the quadratic formula.
Step-by-step explanation:
To determine when the ball reaches the ground, we need to find the time at which the height of the ball is equal to zero. We have the equation h = -16t^2 + 32t + 9, where h represents the height of the ball and t represents time. To find the time, we can set h equal to zero and solve for t:
0 = -16t^2 + 32t + 9
Using the quadratic formula, we can solve for t:
t = (-b ± √(b^2 - 4ac))/(2a)
Plugging in the values from our equation, we get:
t = (-32 ± √(32^2 - 4(-16)(9)))/(2*(-16))
Simplifying, we get two solutions: t = -0.75 and t = 1.625. Since time cannot be negative in this context, the ball reaches the ground at approximately 1.625 seconds.