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 the problem, we need to consider the two components of the SUV's motion: horizontal and vertical.

### 1. **Horizontal Distance**:
The horizontal distance \( d \) can be calculated using the horizontal velocity \( v_x \) and the time \( t \) the SUV was in the air.

\[
d = v_x \times t
\]

Given:
- \( v_x = 50 \, \text{m/s} \)
- \( t = 5 \, \text{seconds} \)

\[
d = 50 \, \text{m/s} \times 5 \, \text{seconds} = 250 \, \text{meters}
\]

So, the SUV falls **250 meters** horizontally from the base of the cliff.

### 2. **Height of the Cliff**:
The height \( h \) of the cliff can be found using the formula for vertical distance under constant acceleration due to gravity:

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

where \( g = 9.8 \, \text{m/s}^2 \) (acceleration due to gravity).

\[
h = \frac{1}{2} \times 9.8 \, \text{m/s}^2 \times (5 \, \text{seconds})^2
\]
\[
h = \frac{1}{2} \times 9.8 \times 25 = 122.5 \, \text{meters}
\]

So, the height of the cliff is **122.5 meters**.

### Summary:
- The SUV landed **250 meters** away horizontally from the base of the cliff.
- The cliff is **122.5 meters** high.

Would you like further details or have any questions?

Here are 5 related questions:
1. How would the horizontal distance change if the SUV's speed were doubled?
2. What would be the effect on the time to hit the ground if the cliff were twice as high?
3. How would air resistance affect the results?
4. How does the gravitational acceleration on Earth compare to other planets?
5. What would happen if the SUV had an initial vertical velocity?

**Tip:** In projectile motion, horizontal and vertical motions are independent of each other. The horizontal motion only depends on the initial speed, while the vertical motion depends on the height and gravity.

Learn how to calculate the horizontal distance traveled and the height of a cliff using projectile motion principles. Includes step-by-step solutions with specific data points. Suitable for students in 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