An SUV drove off a cliff with a horizontal velocity of 50m/s. Suppose it took 5 seconds for the SUV to hit the ground below, how far horizontally from the base of the cliff did the SUV fall? How high is the cliff?

To solve this problem, we'll treat the motion of the SUV as two separate components: horizontal and vertical. 

### Horizontal Motion
The horizontal distance traveled by the SUV can be found using the equation:
\[
\text{Horizontal Distance} = \text{Horizontal Velocity} \times \text{Time}
\]
Given:
- Horizontal velocity (\(v_x\)) = 50 m/s
- Time (\(t\)) = 5 s

\[
\text{Horizontal Distance} = 50 \, \text{m/s} \times 5 \, \text{s} = 250 \, \text{m}
\]
So, the SUV fell 250 meters horizontally from the base of the cliff.

### Vertical Motion
To find the height of the cliff, we'll use the following kinematic equation for vertical motion under constant acceleration (gravity):
\[
\text{Height} = \frac{1}{2} g t^2
\]
Where:
- \(g\) (acceleration due to gravity) = 9.8 m/s²
- Time (\(t\)) = 5 s

\[
\text{Height} = \frac{1}{2} \times 9.8 \, \text{m/s}^2 \times (5 \, \text{s})^2 = \frac{1}{2} \times 9.8 \, \text{m/s}^2 \times 25 \, \text{s}^2 = 122.5 \, \text{m}
\]
So, the height of the cliff is 122.5 meters.

### Summary:
- **Horizontal distance from the base of the cliff**: 250 meters
- **Height of the cliff**: 122.5 meters

Would you like more details or have any other questions?

Here are five related questions you might find interesting:
1. How would the horizontal distance change if the horizontal velocity were doubled?
2. What would happen to the time taken to hit the ground if the cliff were twice as high?
3. How would the SUV's horizontal distance change if gravity were stronger on another planet?
4. Can you determine the SUV's final vertical velocity just before hitting the ground?
5. How would the problem change if the cliff had an initial height of 200 meters?

**Tip:** Always separate horizontal and vertical motions when dealing with projectile motion, as they are independent of each other.

Learn how to calculate the horizontal distance traveled and the height of a cliff when an SUV falls with a given horizontal velocity and time of impact. Includes detailed step-by-step solutions and formulas for projectile motion under gravity. Suitable for advanced high school students.

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