https://file.aiquickdraw.com/mathbot/file/17229263126242opgh38y.jpg

นักไต่หน้าผาคนหนึ่งยืนอยู่ที่ขอบหน้าผา โยนหินขึ้นในแนวดิ่งด้วยความเร็วที่หลุดออกจากมือ u0 = 13.0 m/s ก้อนหินตกกลับลงมาโดยไม่กระทบขอบหน้าผาและในที่สุดตกสู่พื้นเหวด้านล่าง กำหนดให้ตำแหน่งที่ก้อนหินหลุดจากมือเป็นตำแหน่ง y0 = 0.00 m และ กำหนด g = 9.8 m/s2 จากกราฟจงหาเส้นที่แสดงความเร็ว Vy

Based on the provided problem statement and the uploaded graph, it appears we need to analyze the graph to determine which line represents the velocity \( V_y \) of the rock as it falls.

Here's the step-by-step process to solve the problem:

1. **Understanding the Scenario**:
   - A rock is thrown vertically upward with an initial velocity \( u_0 = 13.0 \, \text{m/s} \).
   - The rock eventually falls back down, passing the initial height \( y_0 = 0 \, \text{m} \), and continues to fall below this point.
   - The acceleration due to gravity is \( g = 9.8 \, \text{m/s}^2 \).

2. **Velocity-Time Equation**:
   The velocity of the rock at any time \( t \) can be described by the equation:
   \[
   V_y = u_0 - g t
   \]

3. **Analyzing the Graph**:
   - The graph shows velocity \( V_y \) versus time \( t \).
   - The lines in the graph represent different scenarios or objects, labeled A, B, C, and D.

4. **Finding the Correct Line**:
   - At \( t = 0 \), the velocity \( V_y \) should be \( 13.0 \, \text{m/s} \).
   - As time progresses, the velocity decreases linearly due to the acceleration of gravity.
   - By the time \( t \) reaches the point where the rock has returned to the initial height \( y_0 = 0 \), the velocity will be zero, and it will continue to decrease as it falls below this point.

Let's match the provided graph with this understanding:
- The correct line should start at \( 13.0 \, \text{m/s} \) at \( t = 0 \) and decrease linearly with a slope of \(-9.8 \, \text{m/s}^2 \).

Upon examining the graph, the line labeled **C**:
- Starts at approximately \( 13.0 \, \text{m/s} \) when \( t = 0 \).
- Decreases linearly and aligns with the expected slope due to gravity.

Thus, the line that represents the velocity \( V_y \) of the rock is line **C**.

Would you like more details or have any questions about this solution? 

Here are some related questions you might find interesting:
1. How can we determine the time at which the rock reaches its highest point?
2. What is the velocity of the rock just before it hits the ground?
3. How high does the rock go before it starts to fall back down?
4. How long does it take for the rock to reach the highest point?
5. What is the total time the rock is in the air before it hits the ground?
6. How does the velocity change during the rock's upward and downward motion?
7. Can we calculate the displacement of the rock at any given time?
8. How would the graph change if the rock was thrown with a different initial velocity?

**Tip:** When analyzing motion graphs, always pay close attention to initial conditions and slopes, as they provide crucial information about the motion's characteristics.

Explore the analysis of vertical velocity motion in physics, focusing on finding Vy from an initial velocity u0 = 13.0 m/s. This problem involves kinematics and the velocity-time equation, Vy = u0 - g * t, where g = 9.8 m/s^2. Suitable for high school students studying physics.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation