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While walking between gates at an airport, you notice a child running along a moving walkway. Estimating that the child runs at a constant speed of 2. 4 m/s relative to the surface of the walkway, you decide to try to determine the speed of the walkway itself. You watch the child run on the entire 18-m walkway in one direction, immediately turn around, and run back to his starting point. The entire trip takes a total elapsed time of 32 s. Given this information, what is the speed of the moving walkway relative to the airport terminal?.

Sagot :

The speed of the moving walkway relative to the airport terminal exists at 1.84 m/s.

How to estimate the speed of the moving walkway relative to the airport terminal?

Let x be the speed of the walkway.

(2.8 + x) = speed of child moving in direction of the walkway

(2.8 - x) =  speed of child moving against the direction of the walkway

Travel time = distance/speed

Travel time of child moving in direction of walkway = 23/(2.8+x)

Total elapsed time given = 29s

23/(2.8 + x)+ 23 / (2.8-x) = 29

LCD = (2.8 + x)(2.8 - x)

[tex]23(2.8 - x) + 23(2.8 + x) = 29(2.8 + x)(2.8 -x)[/tex]

simplifying the equation, we get

[tex]23*2.8-23x+23*2.8+23x=29(2.8^2-x^2)[/tex]

[tex]23(2.8+2.8)/29=2.8^2-x^2[/tex]

[tex]x^2=(2.8)^2-(23*5.6)/29)=3.4[/tex]

[tex]x=\sqrt{3.4}=1.84m/s[/tex]

Speed of walkway = 1.84 m/s

The speed of the moving walkway relative to the airport terminal exists at 1.84 m/s.

To learn more about Speed refer to:

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