Question

Becky found a tennis ball outside a tennis court. She picked up the ball and threw it over the fence into

Answer 1

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.

     $\frac{dh}{dt}=\frac{d}{dt}(-16t^2+80t)$

          $=-32t+80$

     $\frac{dh}{dt}=0$

     $-32t+80=0$

     $t=\frac{80}{32}$

     $t=2.5$ seconds

     That means after 2.5 seconds ball will reach the maximum height.

     By substituting $t=2.5$ in the equation,

     $h=-16(2.5)^2+80(2.5)$

     $h=100$ 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