A football player kicks the ball with an initial upward velocity of 60 feet per second. This situation is modeled using the equation h=−16t2+60t+0

Question

, where h is the height in feet and t is the time in seconds. Using this equation, what is the maximum range the ball will reach? Round to the nearest hundredth.(1 point)
feet

Answer 1

To find the maximum height (range) the football will reach using the equation \( h = -16t^2 + 60t + 0 \), we need to determine the vertex of this parabola. The vertex of a parabola in the form \( h = at^2 + bt + c \) can be found using the formula:

\[ t = -\frac{b}{2a} \]

where \( a = -16 \) and \( b = 60 \).

1. Calculate \( t \):

\[ t = -\frac{60}{2(-16)} = -\frac{60}{-32} = \frac{60}{32} = 1.875 \text{ seconds} \]

2. Now substitute \( t = 1.875 \) back into the height equation to find the maximum height \( h \):

\[ h = -16(1.875)^2 + 60(1.875) + 0 \]

3. Calculate \( (1.875)^2 \):

\[ (1.875)^2 = 3.515625 \]

4. Plug it into the height equation:

\[ h = -16(3.515625) + 60(1.875) \] \[ = -56.25 + 112.5 \] \[ = 56.25 \]

So the maximum height the ball will reach is approximately 56.25 feet.