Question

The Apollo's chariot, a rollercoaster at Busch Gardens, moves at 101 feet per second. The equation of the ride can be represented by the equation h(t) = -16t² + 101t + 10. What is the maximum height reached by the ride? Round to the nearest hundredth.

Answer 1

The maximum height reached by the Apollo's Chariot rollercoaster, using the equation h(t) = -16t² + 101t + 10, is found to be approximately 160.39 feet.

Step-by-step explanation:

To find the maximum height reached by the Apollo's Chariot rollercoaster, represented by the equation h(t) = -16t² + 101t + 10, we can use the vertex form of a parabolic equation, as the vertex will give us the peak height (maximum height) of the rollercoaster.

The vertex form of a parabola is given as h(t) = a(t-h)² + k, where (h, k) is the vertex of the parabola. In our case, the equation is already in standard form, and we can find the time t at which the maximum height is reached by using the formula t = -b/(2a) where a and b are coefficients from the given quadratic equation.

Here, a = -16 and b = 101. Plugging these into the formula, we get t = -101/(2 × -16) = 3.15625 seconds. Now we substitute this value back into the original equation to find h(3.15625).

After calculating, we find the maximum height to be approximately 160.39 feet.