To find the maximum height that the football reaches using the given equation \( h = -16t^2 + 60t + 0 \), we need to determine the vertex of the parabola represented by this quadratic equation.
The standard form of a quadratic equation is \( h = at^2 + bt + c \). For our equation:
- \( a = -16 \)
- \( b = 60 \)
- \( c = 0 \)
The time \( t \) at which the maximum height occurs is given by the formula:
\[ t = -\frac{b}{2a} \]
Substituting the values of \( a \) and \( b \):
\[ t = -\frac{60}{2 \times -16} = \frac{60}{32} = 1.875 \text{ seconds} \]
Now we will substitute \( t = 1.875 \) back into the height equation to find the maximum height \( h \):
\[ h = -16(1.875)^2 + 60(1.875) \]
Calculating \( (1.875)^2 \):
\[ (1.875)^2 = 3.515625 \]
Now calculate \( h \):
\[ h = -16(3.515625) + 60(1.875) \] \[ h = -56.25 + 112.5 \] \[ h = 56.25 \text{ feet} \]
Thus, the maximum height that the ball will reach is \( 56.25 \) feet.
So the final answer is:
\[ \boxed{56.25} \]