Answer:
31). Maximum height = 100 feet
32). Time to hit the ground = 5 seconds
Step-by-step explanation:
31). Equation modeling the height 'h' of the ball is,
h = -16t² + 80t
For the maximum height of the ball,
Find the derivative of 'h' with respect to time 't' and equate it to zero.
[tex]\frac{dh}{dt}=\frac{d}{dt}(-16t^2+80t)[/tex]
[tex]=-32t+80[/tex]
[tex]\frac{dh}{dt}=0[/tex]
[tex]-32t+80=0[/tex]
[tex]t=\frac{80}{32}[/tex]
[tex]t=2.5[/tex] seconds
That means after 2.5 seconds ball will reach the maximum height.
By substituting [tex]t=2.5[/tex] in the equation,
[tex]h=-16(2.5)^2+80(2.5)[/tex]
[tex]h=100[/tex] feet
Therefore, maximum height achieved by the ball is 100 feet.
32). If the ball follows the parabolic path,
Time taken by the ball to reach the maximum height = Time taken by the ball to come back to the ground from the maximum height.
Time taken by the ball to hit the ground = 2(2.5) = 5 seconds
