If an average-sized man with a parachute jumps from an airplane, he will fall 
12.5(0.2t − 1) + 20t feet
 in t seconds. How long will it take him to fall 130 feet? (Round your answer to two decimal places.)

The equation for the height \( h(t) \) in feet after \( t \) seconds is given by:

\[
h(t) = 12.5(0.2t - 1) + 20t
\]

We need to find \( t \) such that the total distance fallen equals 130 feet. This means solving:

\[
h(t) = 130
\]

Now, let's simplify the given equation first:

\[
h(t) = 12.5(0.2t - 1) + 20t
\]
\[
= 12.5 \times 0.2t - 12.5 + 20t
\]
\[
= 2.5t - 12.5 + 20t
\]
\[
= 22.5t - 12.5
\]

So, the equation becomes:

\[
22.5t - 12.5 = 130
\]

Now, solve for \( t \):

\[
22.5t = 130 + 12.5
\]
\[
22.5t = 142.5
\]
\[
t = \frac{142.5}{22.5}
\]

Let's calculate the value of \( t \).The time it takes for the man to fall 130 feet is approximately \( t = 6.33 \) seconds.

Would you like more details or have any questions? Here are some related questions to consider:

1. How does the initial velocity affect the falling time in free fall?
2. What would happen if the man had no parachute—how would the equation change?
3. Can we model the same fall with varying air resistance over time?
4. How does the height of the fall impact the total time before hitting the ground?
5. If the man were heavier, would the fall time be shorter or longer?

**Tip:** When solving equations like this, simplifying them step-by-step helps in avoiding errors and keeps the solution process clear.

If an average-sized man with a parachute jumps from an airplane, he will fall 12.5(0.2t − 1) + 20t feet in t seconds. How long will it take him to fall 130 feet? (Round your answer to two decimal places.)

Learn how to solve a linear equation to determine how long it takes a man with a parachute to fall 130 feet. This problem uses algebraic concepts and formulas, including solving a linear equation step-by-step. Ideal for students in Grades 9-11.

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