To determine the maximum height the football will reach, we can use the vertex formula for a quadratic equation in the standard form \( h = at^2 + bt + c \). In this case, \( a = -16 \), \( b = 60 \), and \( c = 0 \).
The formula to find the time \( t \) at which the maximum height occurs is given by:
\[ t = -\frac{b}{2a} \]
Plugging in the values of \( a \) and \( b \):
\[ t = -\frac{60}{2 \times -16} = \frac{60}{32} = 1.875 \text{ seconds} \]
Next, we substitute \( t = 1.875 \) back into the height equation \( h = -16t^2 + 60t + 0 \) to find the maximum height:
\[ h = -16(1.875)^2 + 60(1.875) \]
Calculating \( (1.875)^2 \):
\[ (1.875)^2 = 3.515625 \]
Now substitute this value into the height equation:
\[ h = -16(3.515625) + 60(1.875) \]
Calculating \( -16(3.515625) \):
\[ -16(3.515625) = -56.25 \]
Calculating \( 60(1.875) \):
\[ 60(1.875) = 112.5 \]
Now combine these results:
\[ h = -56.25 + 112.5 = 56.25 \text{ feet} \]
Thus, the maximum height that the ball will reach is:
\[ \boxed{56.25} \text{ feet} \]