Question

The Apollo's chariot, a rollercoaster at Busch gardens, moves at 110 feet per second. The equation of the ride can be represented by the equation h(t)=-16t^2+101t+10. What is the maximum height reached my this ride?

Answer 1

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 $h(t)=-16t^2+101t+10$. 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 $\frac{-b}{2a}$.

$\frac{-101}{2(-16)}=\frac{101}{32}=3.15625$

Now, we will substitute $t=3.15625$ in our equation to find y-coordinate of vertex as:

$h(3.15625)=-16(3.15625)^2+101(3.15625)+10$

$h(3.15625)=-16(9.9619140625)+101(3.15625)+10$

$h(3.15625)=-159.390625+318.78125+10$

$h(3.15625)=169.390625$

$h(3.15625)\approx 169.39$

Therefore, the ride will reach to a maximum height of 169.39 feet.169.39 feet.