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一列长为360m的火车匀速穿过一条长为1800m的隧道，测得火车完全通过隧道需要108s，求：（1）列车内的乘客在车窗上可以看到自己的像，这是由于光的___...

Mar 19, 2024

一列长为360m的火车匀速穿过一条长为1800m的隧道，测得火车完全通过隧道需要108s，求：（1）列车内的乘客在车窗上可以看到自己的像，这是由于光的_________（选填“反射”或“折射”）形成的

Solution

Determine the physical phenomenon responsible for the formation of images

Answer

反射

Key Concept

Reflection of light is the phenomenon responsible for the formation of images on surfaces like mirrors or windows. When light rays hit a reflective surface, they bounce back, and this can create an image that passengers can see.

Explanation

The image seen by passengers in the train window is formed due to the reflection of light from the window acting like a mirror. This is a common occurrence when light encounters a smooth and shiny surface.

（2）求火车的运行速度；

Solution

Calculate the total distance the train travels to completely pass through the tunnel

Use the average velocity formula:

v_{\text{avg}} = \frac{\Delta x}{\Delta t}

to find the train's velocity

Answer

The train's velocity is 19 m/s.

Key Concept

Kinematics and Average Velocity: The average velocity is calculated by dividing the total displacement by the total time taken for that displacement.

Explanation

To find the train's velocity, we add the length of the train to the length of the tunnel to get the total distance traveled. Then we divide this distance by the time taken to find the average velocity.

（3）穿过隧道后，列车以相同的速度继续前进，面对山崖鸣笛一声，2s后听到回声，求听到回声时距山崖多远？

Solution

Calculate the distance the sound travels: The sound travels to the cliff and back in 2 seconds. Since sound travels at approximately

343 \, \text{m/s}

in air at room temperature, the total distance traveled by the sound is

d_{\text{sound}} = v_{\text{sound}} \times t = 343 \, \text{m/s} \times 2 \, \text{s}

Find the distance to the cliff: The sound travels to the cliff and back, so the distance to the cliff is half the total distance.

d_{\text{cliff}} = \frac{d_{\text{sound}}}{2} = \frac{343 \, \text{m/s} \times 2 \, \text{s}}{2}

Answer

343 meters

Key Concept

The speed of sound in air and the time it takes for sound to travel a certain distance are used to calculate the distance to an object when hearing an echo.

Explanation

The echo's travel time is used to calculate the total distance the sound wave travels, which is then halved to find the distance to the reflecting object, in this case, the cliff.