A boulder moving horizontally at 32.4 meters per second on flat ground rolls off of a 25.6 meter high cliff. How much time does it take for the boulder to reach the ground? Time equals blank seconds; fill in the blank.

This problem involves finding the time it takes for a boulder to fall from a cliff with a vertical height of 25.6 meters. Since the motion in the horizontal direction does not affect the vertical motion, we can focus only on the vertical fall. 

We can use the following kinematic equation to solve for the time \( t \):

\[
d = \frac{1}{2} g t^2
\]

Where:
- \( d \) is the vertical distance (25.6 m),
- \( g \) is the acceleration due to gravity (approximately \( 9.8 \, \text{m/s}^2 \)),
- \( t \) is the time in seconds.

### Solving for \( t \):
Rearranging the equation to solve for \( t \):

\[
t = \sqrt{\frac{2d}{g}} 
\]

Substituting the known values:

\[
t = \sqrt{\frac{2 \times 25.6}{9.8}} 
\]

Let's calculate that.

The time it takes for the boulder to reach the ground is approximately \( 2.29 \) seconds.

Would you like more details or have any questions?

Here are 5 related questions:
1. How far does the boulder travel horizontally before hitting the ground?
2. What is the boulder's vertical velocity just before hitting the ground?
3. How would the time change if the cliff were twice as high?
4. What is the total velocity of the boulder just before it hits the ground?
5. How does air resistance affect the time of flight in this scenario?

**Tip:** In free-fall problems, the horizontal and vertical motions are independent of each other. This allows us to treat the vertical and horizontal components separately.

A boulder moving horizontally at 32.4 meters per second on flat ground rolls off of a 25.6 meter high cliff. How much time does it take for the boulder to reach the ground?

Learn how to calculate the time it takes for a boulder to fall from a 25.6 meter high cliff with a horizontal velocity of 32.4 m/s. Using kinematic equations, this problem illustrates key concepts in free-fall and vertical motion. Suitable for high school students in Grades 9-12.

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