A Boeing 747 "Jumbo Jet" has a length of 59.7 m. The runway on which the plane lands intersects another runway. The width of the intersection is 25.0 m. The plane decelerates through the intersection at a rate of 5.4 m/s2 and clears it with a final speed of 53 m/s. How much time is needed for the plane to clear the intersection?

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aristocles aristocles · Answer 1 · 2019-09-12T02:07:32+02:00

Answer:

t = 1.48 s

Explanation:

As we know that length of the Boeing plane is

[tex]L = 59.7 m[/tex]

width of the intersection is given as

[tex]w = 25.0 m[/tex]

now we know that deceleration of the plane is given as

[tex]a = -5.4 m/s^2[/tex]

Also the final speed of the plane while it clears the intersection is given as

[tex]v_f = 53 m/s[/tex]

now we have

[tex]d = (\frac{v_f + v_i}{2}) t[/tex]

[tex](25 + 59.7) = (\frac{53 + v_i}{2}) t[/tex]

also we know that

[tex]v_f - v_i = at[/tex]

[tex]53 - v_i = -5.4 t[/tex]

now we have

[tex]84.7 = (\frac{53 + 53 + 5.4t}{2})t[/tex]

by solving above equation we have

[tex]t = 1.48 s[/tex]