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 21.3 m. The plane decelerates through the intersection at a rate of 5.33 m/s2 and clears it with a final speed of 38.3 m/s. How much time is needed for the plane to clear the intersection?

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To calculate the time needed for the plane to clear the intersection, we can use the equation of motion:

v^2 = u^2 + 2as

where:
v = final velocity (38.3 m/s)
u = initial velocity (unknown)
a = acceleration (-5.33 m/s^2)
s = distance (length of the plane - width of the intersection)

Let's calculate the initial velocity first:

u^2 = v^2 - 2as
u^2 = (38.3 m/s)^2 - 2(-5.33 m/s^2)(59.7 m - 21.3 m)
u^2 = 1468.89 m^2/s^2 - 2(-5.33 m/s^2)(38.4 m)
u^2 = 1468.89 m^2/s^2 + 2(5.33 m/s^2)(38.4 m)
u^2 = 1468.89 m^2/s^2 + 409.27 m^2/s^2

u^2 = 1878.16 m^2/s^2

Taking the square root of both sides, we find:

u = √(1878.16 m^2/s^2)
u ≈ 43.32 m/s

Now that we have the initial velocity, we can calculate the time needed to clear the intersection using the equation of motion:

v = u + at

38.3 m/s = 43.32 m/s + (-5.33 m/s^2)t

Rearranging the equation, we have:

-5.33 m/s^2 t = 38.3 m/s - 43.32 m/s
-5.33 m/s^2 t = -5.02 m/s

Dividing both sides by -5.33 m/s^2, we get:

t = (-5.02 m/s) / (-5.33 m/s^2)
t ≈ 0.942 seconds

Therefore, it takes approximately 0.942 seconds for the plane to clear the intersection.

To find the time needed for the plane to clear the intersection, we can use the equation of motion:

s = ut + (1/2)at^2

where:
s = displacement or distance (59.7 m)
u = initial velocity (38.3 m/s)
a = acceleration (deceleration) (-5.33 m/s^2)
t = time

Rearranging the equation, we get:

t = √(2s/a)

Let's substitute the values and calculate.

t = √(2 * 59.7 / -5.33)
t ≈ √(11.248 / -5.33)
t ≈ √(-2.1108)

Since the result is negative, it means there was an error in the given information or calculation. Deceleration cannot create a negative time value, so please recheck the numbers or the question.