To find the maximum height reached by the football after it is kicked, we can derive it from the given quadratic equation for height:
\[ h(t) = -16t^2 + 60t + 0 \]
This is a quadratic equation in the standard form \( h(t) = at^2 + bt + c \), where:
- \( a = -16 \)
- \( b = 60 \)
- \( c = 0 \)
The maximum value of a quadratic function occurs at the vertex, which can be found using the formula:
\[ t = -\frac{b}{2a} \]
Substituting the values for \( a \) and \( b \):
\[ t = -\frac{60}{2(-16)} = -\frac{60}{-32} = \frac{60}{32} = 1.875 \text{ seconds} \]
Next, we can substitute this value of \( t \) back into the height equation to find the maximum height:
\[ h(1.875) = -16(1.875)^2 + 60(1.875) \]
Calculating \( (1.875)^2 \):
\[ (1.875)^2 = 3.515625 \]
Now substitute this back into the equation for height:
\[ h(1.875) = -16(3.515625) + 60(1.875) \] \[ h(1.875) = -56.25 + 112.5 \] \[ h(1.875) = 56.25 \text{ feet} \]
Thus, the maximum height that the ball will reach is 56.25 feet.