A boulder moving horizontally at 9.83 meters per second on flat ground rolls off of a 47.9 meter high cliff. How far from the base of the cliff does the boulder land? Delta x equals blank meters; fill in the blank.

To solve this problem, we can break the motion of the boulder into two parts: horizontal and vertical.

### Step 1: Vertical Motion
In the vertical direction, the only force acting on the boulder is gravity. We can use the following kinematic equation to determine the time it takes for the boulder to fall from the cliff:

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

Where:
- \( y = 47.9 \, \text{m} \) (height of the cliff),
- \( g = 9.81 \, \text{m/s}^2 \) (acceleration due to gravity),
- \( t \) is the time in seconds.

Solving for \( t \):

\[
47.9 = \frac{1}{2} \times 9.81 \times t^2
\]

\[
t^2 = \frac{47.9 \times 2}{9.81}
\]

\[
t^2 = 9.765
\]

\[
t = \sqrt{9.765} \approx 3.12 \, \text{seconds}
\]

### Step 2: Horizontal Motion
Now that we know the boulder is in the air for \( 3.12 \, \text{seconds} \), we can calculate how far it travels horizontally. The horizontal velocity of the boulder is constant at \( 9.83 \, \text{m/s} \), so we use:

\[
\Delta x = v_x \cdot t
\]

Where:
- \( v_x = 9.83 \, \text{m/s} \),
- \( t = 3.12 \, \text{seconds} \).

\[
\Delta x = 9.83 \times 3.12 \approx 30.68 \, \text{meters}
\]

### Answer:
The boulder lands **30.68 meters** from the base of the cliff.

Would you like more details or have any questions?

### Related Questions:
1. How does increasing the height of the cliff affect the distance traveled by the boulder?
2. What would happen if the boulder had an initial vertical velocity as well?
3. How would air resistance alter the result of this problem?
4. How do you calculate the velocity of the boulder when it hits the ground?
5. How would the solution change if the acceleration due to gravity was not constant?

### Tip:
Always break down projectile motion problems into horizontal and vertical components to simplify your calculations.

Learn how to solve a projectile motion problem involving a boulder moving at 9.83 m/s horizontally and rolling off a 47.9-meter-high cliff. This solution covers vertical and horizontal motion calculations, using kinematic equations and concepts suitable for Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation