Question

2. In an algebra class, students were given the function h(t) = 80t - 16t² tomodel a golf ball's height, h, in feet after being hit, where t is time inseconds. Students were then to write a true statement about thesituation modeled. Diana said that the ball reaches a maximum height of96 feet. Katie said the ball hits the ground after 5 seconds. Whichstatement is true?ADiana is correct.B. Katie is correct.c. Both Diana and Katie are correct.D. Neither Diana nor Katie is correct.

Answer 1

Step 1

Given;

`h(t)=80t-16t^2`

Used to model a golf ball's height, h, in feet after being hit, where t is time in seconds. Students were then to write a true statement about the

situation modeled. Diana said that the ball reaches a maximum height of

96 feet. Katie said the ball hits the ground after 5 seconds. Which

statement is true?

Step 2

To find the maximum height, we solve for the vertex (h,k)

`\begin{gathered} h=-(b)/(2a)=-(80)/(2(-16))=(-80)/(-32)=2.5 \\ k=80(2.5)-16(2.5)^2 \\ k=200-100=100 \end{gathered}`

Thus, the maximum height is 100 feet.

Diana said that the ball reaches a maximum height of

96 feet. This statement is false.

To find when the ball will hit the ground we equate h(t) to 0

`\begin{gathered} 80t-16t^2=0 \\ t(80-16t)=0 \\ t=0\text{ } \\ or \\ 80-16t=0 \\ 80=16t \\ t=5 \end{gathered}`

Thus the ball will hit the ground after 5 seconds

Answer; Katie is correct. The ball will hit the ground after 5 seconds.

Option B