Question

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
, 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)

Answer 1

To find the maximum height (or the apex) that the ball reaches, we can use the vertex formula for a parabola given by the equation \( h = -16t^2 + 60t + 0 \). The general formula for the time \( t \) at which the maximum height occurs in a quadratic equation \( ax^2 + bx + c \) is given by:

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

In this case, \( a = -16 \) and \( b = 60 \). Plugging in the values:

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

Next, we substitute \( t = 1.875 \) back into the height equation to find the maximum height:

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

Calculating \( (1.875)^2 \):

\[
(1.875)^2 = 3.515625
\]

Now, substituting this value into the equation:

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

Calculating each term:

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

Combining the terms:

\[
h = -56.25 + 112.5 = 56.25
\]

Thus, the maximum height the ball will reach is **56.25 feet**.