Answers:
1. 25
2. 1.25
3. 2.5
Step-by-step explanation:
The equation that models the height of the ball is h(t) = -16t² + 40t
This is an equation of a parabola, so the maximum height occurs at the vertex of the parabola. The first coordinate for the vertex is t = -b/2a
Where b is the number besides t and a is the number besides t².
Therefore, a = -16 and b = 40, and the ball reaches its maximum height at
t = -40/2(-16)
t = -40/(-32)
t = 1.25
Now, we can calculate the maximum height replacing t = 1.25 on the equation for h(t)
h(t) = -16t² + 40t
h(1.25) = -16(1.25)² + 40(1.25)
h(1.25) = -25 + 50
h(1.25) = 25
Finally, the ball falls back to the ground when the height is 0, so we need to solve the equation
h(t) = -16t² + 40t = 0
Solving for t, we get:
-16t² + 40t = 0
t(-16t + 40) = 0
Then,
t = 0
or
-16t + 40 = 0
-16t + 40 - 40 = 0 - 40
-16t = -40
-16t/(-16) = -40/(-16)
t = 2.5
Therefore, the ball falls back to the ground at 2.5