During a long airport layover, a physicist father and his 8-year-old daughter try a game that involves a moving walkway. They have measured the walkway to be 41.5 m long. The father has a stopwatch and times his daughter. First, the daughter walks with a constant speed in the same direction as the conveyor. It takes 15.1 s to reach the end of the walkway. Then, she turns around and walks as before with the same speed relative to the conveyor, just this time in the opposite direction. The return leg takes 72.1 s.

a) What is the speed of the walkway conveyor relative to the terminal?

b) With what speed was the girl walking?

a) To find the speed of the walkway conveyor relative to the terminal, we can use the equation:

Speed = Distance / Time

First, let's find the speed of the girl when walking in the same direction as the conveyor. The distance covered in this case is the length of the walkway, which is 41.5 m. The time taken is 15.1 s.

Speed of the girl walking in the same direction = 41.5 m / 15.1 s

Next, let's find the speed of the girl when walking in the opposite direction. Again, the distance covered is the length of the walkway, which is 41.5 m. The time taken is 72.1 s.

Speed of the girl walking in the opposite direction = 41.5 m / 72.1 s

Now, we know that the speed of the walkway conveyor relative to the terminal is the difference between the speed of the girl walking in the same direction and the speed of the girl walking in the opposite direction. So, we can subtract these two speeds to find the speed of the walkway conveyor.

Speed of the walkway conveyor relative to the terminal = Speed of the girl walking in the same direction - Speed of the girl walking in the opposite direction

b) To find the speed of the girl walking, we need to assume that the speed of the walkway conveyor is constant (which is typically the case). We can then use the speed of the girl walking in the same direction as the conveyor (which we calculated in part a) using the equation:

Speed = Distance / Time

Speed of the girl walking = Distance / Time

In this case, the distance covered is the length of the walkway, which is 41.5 m. The time taken is 15.1 s.

Speed of the girl walking = 41.5 m / 15.1 s

To summarize:

a) The speed of the walkway conveyor relative to the terminal is the difference between the speed of the girl walking in the same direction and the speed of the girl walking in the opposite direction.

b) The speed of the girl walking is the distance covered divided by the time taken, assuming the speed of the walkway conveyor is constant.