A rock is thrown from one side of a river to another. The function h(t) = -16t^2 + 80t + 30 gives the height in inches of the rock t seconds after it has been thrown. Find h (2.5)

Answer 1

To find the height of the rock at \( t = 2.5 \) seconds, we will substitute \( t = 2.5 \) into the function \( h(t) \).

The function given is:

\[ h(t) = -16t^2 + 80t + 30 \]

Now, substituting \( t = 2.5 \):

\[ h(2.5) = -16(2.5)^2 + 80(2.5) + 30 \]

First, calculate \( (2.5)^2 \):

\[ (2.5)^2 = 6.25 \]

Now, substitute this back into the equation:

\[ h(2.5) = -16(6.25) + 80(2.5) + 30 \]

Calculate each term:

1. \( -16(6.25) = -100 \)
2. \( 80(2.5) = 200 \)

Now combine these values:

\[ h(2.5) = -100 + 200 + 30 \]

Now simplify:

\[ h(2.5) = 130 \]

So, the height of the rock at \( t = 2.5 \) seconds is:

\[ \boxed{130} \text{ inches} \]