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The problem states that an eagle is dropping a mouse from a height of 730 meters, at a descent angle of \(50^\circ\) from the vertical. The mouse reaches the ground after 5 seconds, and we are asked to find the horizontal distance the mouse travels during this time.

### Step-by-step solution:

1. **Understanding the motion**:
   - The vertical motion is affected by gravity, while the horizontal motion is constant (because there's no horizontal acceleration).
   - The mouse's total motion is at an angle of \(50^\circ\) with the vertical. Therefore, the components of the velocity must be split into horizontal and vertical components.

2. **Calculate the vertical distance**:
   - Given the height of 730 meters and the time to hit the ground (5 seconds), we can calculate the initial vertical velocity component \( v_{y0} \).
   - Using the kinematic equation for vertical motion:
   \[
   h = v_{y0} t + \frac{1}{2} g t^2
   \]
   Where:
   - \( h = 730 \, \text{m} \) (height)
   - \( t = 5 \, \text{seconds} \) (time)
   - \( g = 9.8 \, \text{m/s}^2 \) (acceleration due to gravity)

3. **Calculate the initial velocity**:
   - To find the total velocity \( v_0 \), we need to use the angle information.
   - Once we have the total initial velocity, we can calculate the horizontal velocity component \( v_{x0} \) as \( v_{x0} = v_0 \sin(50^\circ) \).

4. **Calculate the horizontal distance**:
   - The horizontal distance \( d \) is given by the equation:
   \[
   d = v_{x0} t
   \]
   Using the time \( t = 5 \, \text{seconds} \).

Let's proceed to calculate these quantities.The horizontal distance the mouse travels is approximately 724 meters. This corresponds to option **B** in the provided choices.

Would you like further details or explanations? 

Here are some related questions to consider:
1. How is the initial velocity determined in projectile motion?
2. What would happen if the angle of descent changed?
3. How does the time of fall affect the horizontal distance?
4. What other factors, such as air resistance, could affect the mouse's motion?
5. How would the calculations change if the eagle dropped the mouse from a greater height?

**Tip**: For projectile motion, it's important to always separate the horizontal and vertical components of motion to simplify calculations.

Một con đại bàng đang quắp một con chuột và bay nhào xuống dưới góc 50 độ so với phương thẳng đứng và thả rơi con chuột từ độ cao 730 m. Sau 5 giây thì con chuột chạm đất. Hỏi con chuột bay được bao xa theo phương ngang?

This problem explores projectile motion where an eagle drops a mouse from a height of 730 meters at a descent angle of 50 degrees. The mouse takes 5 seconds to hit the ground, and we calculate the horizontal distance traveled. The solution covers kinematic equations for vertical and horizontal motion. Suitable for students in Grades 10-12.

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