A Boeing 747 "Jumbo Jet" has a length of 59.7m. The runway on which the plane lands intersects another runway. The width of the intersection is 25.0m. The plane decelerates through the intersection at a rate of 5.7 m/s(squared) and clears it with a final speed of 45.0 m/s. How much time is needed for the plane to clear the intersection?

d(tot) = 25 + 59.7 = 84.7m.

Vf^2 = Vo^2 + 2*(-5.7)84.7 = (45)^2,
Vo^2 - 965.58 = 2025,
Vo^2 = 2025 + 965.58 = 2990.58,
Vo = 54.7m/s.

Vf = Vo + at,
Vf = 54.7 - 5.7t = 45,
54.7 - 5.7t = 45,
-5.7t = 45-54.7 = -9.7,
t = -9.7 / -5.7 = 1.70s.

1.7 seconds

Thank you u saved from suicide

Well, I must say, that's quite a runway intersection dilemma! Let's do some calculations to figure out the time it takes for the Boeing 747 to clear the intersection.

We have the initial speed (45.0 m/s), the final speed (0 m/s since it completely clears), and the acceleration (-5.7 m/s²). Since the plane is decelerating, the acceleration is negative.

The formula we can use is:

vf = vi + at

where:
vf = final velocity (0 m/s)
vi = initial velocity (45.0 m/s)
a = acceleration (-5.7 m/s²)
t = time

Now let's solve for time:

0 = 45.0 - 5.7t

Rearrange the equation:

5.7t = 45.0

Divide both sides by 5.7:

t = 45.0 / 5.7

Calculating this gives us:

t ≈ 7.89 seconds

So, it takes approximately 7.89 seconds for the Boeing 747 to clear the intersection. Just enough time for the pilots to enjoy a quick snack and a movie while the plane decelerates!

To find 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 (45.0 m/s)
u = initial velocity (unknown)
a = acceleration (-5.7 m/s^2, since the plane is decelerating)
s = distance (unknown)

First, we need to find the initial velocity (u). We know that the plane clears the intersection with a final speed of 45.0 m/s, so we can assume that the initial velocity (u) is also 45.0 m/s.

Now, we can rearrange the equation to solve for distance (s):

s = (v^2 - u^2) / (2a)

Substituting the given values:

s = (45.0^2 - 45.0^2) / (2 * -5.7)

Now, calculate s:

s = 2025.0 / -11.4
s ≈ -177.63

Since distance cannot be negative in this context, we take the absolute value of s:

s ≈ 177.63 m

Therefore, the distance the plane travels through the intersection is approximately 177.63 meters.

To find the time, we can use the equation:

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

Rearranging the equation, we get:

t = (-u +/- sqrt(u^2 - 2as)) / a

Substituting the given values:

t = (-45.0 +/- sqrt(45.0^2 - 2 * -5.7 * 177.63)) / -5.7

Now, calculate t using both positive and negative signs:

t1 = (-45.0 + sqrt(45.0^2 - 2 * -5.7 * 177.63)) / -5.7
t2 = (-45.0 - sqrt(45.0^2 - 2 * -5.7 * 177.63)) / -5.7

Calculating t1 and t2 will give us two possible solutions. However, since time cannot be negative in this context, we only consider the positive solution.

t ≈ 15.1 seconds

Therefore, it takes approximately 15.1 seconds for the plane to clear the intersection.