Answer:
169.39 feet.
Step-by-step explanation:
We have been given that the Apollo's chariot, a roller coaster at Busch gardens, moves at 110 feet per second. The equation of the ride can be represented by the equation [tex]h(t)=-16t^2+101t+10[/tex]. We are asked to find the maximum height that the ride can reach.
To find the maximum height that the ride can reach, we need to find y-coordinate of vertex of parabola because our given equation is downward opening parabola and its maximum point will be the vertex.
First of all, we will find x-coordinate of vertex using formula [tex]\frac{-b}{2a}[/tex].
[tex]\frac{-101}{2(-16)}=\frac{101}{32}=3.15625[/tex]
Now, we will substitute [tex]t=3.15625[/tex] in our equation to find y-coordinate of vertex as:
[tex]h(3.15625)=-16(3.15625)^2+101(3.15625)+10[/tex]
[tex]h(3.15625)=-16(9.9619140625)+101(3.15625)+10[/tex]
[tex]h(3.15625)=-159.390625+318.78125+10[/tex]
[tex]h(3.15625)=169.390625[/tex]
[tex]h(3.15625)\approx 169.39[/tex]
Therefore, the ride will reach to a maximum height of 169.39 feet.169.39 feet.
