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?.

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tutorconsortium31 tutorconsortium31 · Answer 1 · 2022-08-05T21:18:42+02:00

Speed of walkway = 1.84 m/s

let x=speed of walkway

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

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

Travel time=distance/speed

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

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)

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

23*2.8-23x+23*2.8+23x=29(2.8^2-x^2)

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

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

x=sqrt(3.4)=1.84m/s

Speed of walkway = 1.84 m/s

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