Angel Falls in southeastern Venezuela is the highest waterfall in the world, falling from a 979m height. If it takes 14 seconds for the water to fall from the top to the river below, and lands 50 meters from the base of the mountain, what is the horizontal speed at the top?

To determine the horizontal speed of the water at the top of Angel Falls, we can analyze the situation as a projectile motion problem.

### Given Data:
- Height of the waterfall: \( h = 979 \, \text{m} \)
- Time of fall: \( t = 14 \, \text{seconds} \)
- Horizontal distance: \( x = 50 \, \text{m} \)

### Step-by-Step Approach:
1. **Vertical Motion**: The time of the fall is determined by the vertical motion. Since we know the height and time of the fall, we can verify the time with the formula for the vertical fall under gravity:
   \[
   h = \frac{1}{2} g t^2
   \]
   where \( g = 9.8 \, \text{m/s}^2 \) is the acceleration due to gravity, and \( h \) is the vertical displacement.

   Solving for \( t \):
   \[
   979 = \frac{1}{2} \times 9.8 \times t^2
   \]
   \[
   t^2 = \frac{2 \times 979}{9.8}
   \]

2. **Horizontal Motion**: Assuming the horizontal speed of the water at the top is constant (no horizontal acceleration), the horizontal distance \( x \) is related to the horizontal speed \( v_x \) and time \( t \) by the equation:
   \[
   x = v_x \times t
   \]
   Solving for \( v_x \):
   \[
   v_x = \frac{x}{t}
   \]

Now, let's calculate the horizontal speed \( v_x \).The horizontal speed of the water at the top of Angel Falls is approximately \( 3.57 \, \text{m/s} \).

Would you like more details on this calculation, or do you have any further questions?

Here are 5 related questions to deepen your understanding:
1. How does the time of fall relate to the height of a waterfall?
2. What would happen to the horizontal speed if the horizontal distance increased?
3. Can we calculate the speed of the water when it hits the ground?
4. How does air resistance affect the horizontal and vertical motion of the water?
5. How would the horizontal speed change if the waterfall height were different?

**Tip:** In projectile motion, horizontal and vertical motions are independent of each other, except for the shared time of flight.

Learn how to calculate the horizontal speed of water at the top of Angel Falls using projectile motion principles. This problem involves determining horizontal velocity from given vertical height and time of fall data.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation