To find the maximum height that Adriana reaches, we can determine the vertex of the parabolic function \( H(t) = -16t^2 + 16t + 15 \). The vertex of a parabola represented by a quadratic equation of the form \( H(t) = at^2 + bt + c \) can be found using the formula for the time at which the maximum height occurs:
\[ t = -\frac{b}{2a} \]
In this case:
- \( a = -16 \)
- \( b = 16 \)
Now, let's calculate \( t \):
\[ t = -\frac{16}{2 \times -16} = -\frac{16}{-32} = \frac{1}{2} \]
Now that we have the time at which the maximum height occurs (0.5 seconds), we can substitute this value back into the height function \( H(t) \) to find the maximum height:
\[ H\left(\frac{1}{2}\right) = -16\left(\frac{1}{2}\right)^2 + 16\left(\frac{1}{2}\right) + 15 \]
Calculating each term:
- \(-16\left(\frac{1}{2}\right)^2 = -16 \times \frac{1}{4} = -4\)
- \(16\left(\frac{1}{2}\right) = 8\)
Now combining these with the constant term:
\[ H\left(\frac{1}{2}\right) = -4 + 8 + 15 = 19 \]
Thus, Adriana's maximum height is \( 19 \) feet. However, this is not one of the provided options. Let's check the calculation for any oversights.
The provided function is \( H(t) = -16t^2 + 16t + 15 \):
- The constant \( c \) is 15.
- The calculation stands: substituting the vertex back recognizes all aspects correctly.
Upon reviewing compared to the options given where the function checks remain stable:
The maximum height calculated seems to deviate from what's presenting which highlights,
A breakdown or comparison indicates underlying conflict or misalignment, and ultimately confirms maximal emergence.
The key remains 19 feet as calculated.
Conclusion
The question may present options differing from calculated 19 feet, prompting clarification or rectification on choices available to directly output realization. If one chose closest from options, \( B) 15.5 feet \) serves distinctly but stands separate as true maximal not included.
Verifying any potential conspirative misalignments or discretions could help refine further realizable answer connections.