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We are given a scenario where a skydiver jumps from an altitude of 2,500 ft and opens his parachute at an altitude of 1,000 ft. The equation provided models the skydiver's height \( h(t) \) over time as:

\[
h(t) = -16t^2 + v_0t + h_0
\]

Where:
- \( v_0 = 0 \) ft/s (initial velocity, since the jumper is falling from rest),
- \( h_0 = 2500 \) ft (initial height),
- \( h(t) = 1000 \) ft (height when the parachute is opened),
- \( g = 32 \, \text{ft/s}^2 \) is the acceleration due to gravity, with the constant \( -16t^2 \) representing half of \( g \).

### Solving for time \( t \)

We substitute the known values into the equation:
\[
1000 = -16t^2 + 2500
\]

Rearrange the equation to solve for \( t^2 \):
\[
-16t^2 = 1000 - 2500
\]
\[
-16t^2 = -1500
\]
\[
t^2 = \frac{1500}{16}
\]
\[
t^2 = 93.75
\]
\[
t = \sqrt{93.75} \approx 9.68 \, \text{seconds}
\]

Thus, the time the jumper falls before opening the parachute is approximately \( 9.7 \) seconds.

### Answer:
The correct answer is **9.7 s**.

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Do you want any more details or have any questions about this problem?

Here are 5 related questions to expand your understanding:

1. How would the time change if the initial altitude were different?
2. What would happen if the skydiver had an initial downward velocity?
3. Can you derive the formula \( h(t) = -16t^2 + v_0t + h_0 \) from basic physics principles?
4. How would air resistance alter the time before the parachute is opened?
5. What if the skydiver opens the parachute at a lower altitude? How would that affect the calculation?

**Tip:** Always check units when solving physics problems to ensure consistency across all terms in an equation.

A skydiver jumps from an airplane at an altitude of 2,500 ft. He falls under the force of gravity until he opens his parachute at an altitude of 1,000 ft. Using the initial velocity of zero, approximately how long does the jumper fall before he opens his chute?

This problem involves a skydiver jumping from 2,500 ft and opening the parachute at 1,000 ft. Learn how to use a quadratic equation to calculate the time it takes before the parachute opens, utilizing principles of algebra and kinematics.

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