A Boeing 747 \"Jumbo Jet\" has a length of 56.7 m. The runway on which the plane

Question

A Boeing 747 "Jumbo Jet" has a length of 56.7 m. The runway on which the plane lands intersects another runway. The width of the intersection is 26.5 m. The plane decelerates through the intersection at a rate of 5.77 m/s2 and clears it with a final speed of 44.8 m/s. How much time is needed for the plane to clear the intersection?(Note that the plane enters the intersection when any part of the plane is in the intersection and blocking the other runway. The plane clears the intersection when there is no longer any part of the plane in the intersection blocking the other runway.)

Explanation / Answer

Use the equation, vf^2 = vi^2 + 2ad. Where vf is the final velocity, vi is the initial velcoity a is the accelaration and d is the distance traversed. You first want to find the initial velocity (vi) BEFORE the plane entered the intersection.

Note that when I plugged in the values below, I added the width of the intersection PLUS the length of the aircraft. That's because the speed they give is when the entire aircraft clears the intersection. That means the aircraft traveled the width of the intersection AND it's own length.

Also, note that acceleration is negative since the plane is slowing down.

(44.8 m/s)^2 = vi^2 + 2 (-5.77 m/s^2) (26.5m + 56.7m)

vi = 54.47m/s

Now, you can use vf = vi + at. Where vf = final velocity, vi = initial velocity and t = time in seconds and a = acceleration.

44.8 = 54.47 - 5.77t. Solving this equation gives t = 1.676 s.

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