The height of the football as a function of time is given by the equation:
\[ h = -16t^2 + 60t + 0 \]
To find the maximum height, we need to determine the vertex of the parabola represented by this equation. The formula for the time \( t \) at which the maximum height occurs (the vertex) for a quadratic equation in the standard form \( h = at^2 + bt + c \) is given by:
\[ t = -\frac{b}{2a} \]
In this equation:
- \( a = -16 \)
- \( b = 60 \)
Substituting the values of \( a \) and \( b \):
\[ t = -\frac{60}{2 \cdot -16} = \frac{60}{32} = \frac{15}{8} = 1.875 \text{ seconds} \]
Next, we will substitute \( t = 1.875 \) back into the original height equation to find the maximum height:
\[ h = -16(1.875)^2 + 60(1.875) \]
Calculating \( (1.875)^2 \):
\[ (1.875)^2 = 3.515625 \]
Now substituting that value back in:
\[ h = -16(3.515625) + 60(1.875) \] \[ h = -56.25 + 112.5 \] \[ h = 56.25 \text{ feet} \]
Therefore, the maximum height the ball will reach is:
\[ \boxed{56.25} \text{ feet} \]