Answer
$\approx$74.3 feet
Work Step by Step
To find the height of the geyser at any time, we will use the equation: $s= ut+(1/2)at^2$
Next, we simply plug in our given variables.
$h= 69t +(1/2)(-32.174)t^2$ This then simplifies to:
$h =69t - 16.09t^2$
This formula represents a quadratic formula that will have a maximum value.
Use the axis of symmetry formula, -b/2a, and plug in the variables accordingly.
$$ 69/2(16.09) \\ \approx2.14$$
Plug this value in for t to find h in the quadratic equation.
$$h =69(2.14)-16.09(2.14)^2 \\ \approx 74.3$$
