A moving sidewalk in a busy airport terminal moves 1 m/s and is 200 m long. A passenger steps onto one end and walks, in the same direction as the sidewalk is moving, at a rate of 2.0 m/s relative to the moving sidewalk. How much time does it take the passenger to reach the opposite end of the walkway?

To determine how long it takes the passenger to reach the opposite end of the moving sidewalk, we first need to calculate the passenger's effective speed relative to the ground. Since the passenger is walking in the same direction as the sidewalk is moving, we can simply add their speeds together.

Calculating Effective Speed

The speed of the moving sidewalk is 1 m/s, and the passenger's walking speed relative to the sidewalk is 2.0 m/s. Therefore, the total speed of the passenger relative to the ground is:

• Speed of sidewalk: 1 m/s
• Walking speed of passenger: 2.0 m/s
• Total speed of passenger: 1 m/s + 2.0 m/s = 3.0 m/s

Finding the Time Taken

Now that we know the passenger's effective speed is 3.0 m/s, we can calculate the time it takes to travel the length of the sidewalk, which is 200 m. The formula to find time is:

Time = Distance / Speed

Substituting the known values:

• Distance = 200 m
• Speed = 3.0 m/s

Thus, the time taken is:

Time = 200 m / 3.0 m/s = 66.67 seconds

Final Thoughts

So, it will take the passenger approximately 66.67 seconds to reach the opposite end of the moving sidewalk. This example illustrates how combining speeds can simplify the process of calculating travel times in scenarios involving moving platforms or vehicles. Understanding these concepts can be quite useful in various real-life situations, such as when planning travel or understanding motion in physics.