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A Boeing 747 Jumbo Jet has a length of 59.7 $\mathrm{m}$ . The runway on which the plane lands intersects another runway. The width of the inter- section is 25.0 $\mathrm{m}$ . The plane decelerates through the intersection at a rate of 5.70 $\mathrm{m} / \mathrm{s}^{2}$ and clears it with a final speed of 45.0 $\mathrm{m} / \mathrm{s}$ . How much time is needed for the plane to clear the intersection?

So 1.69 second is needed for the plane to clear the intersection.

Physics 101 Mechanics

Chapter 2

Kinematics in One Dimension

Motion Along a Straight Line

Cornell University

University of Washington

Hope College

Lectures

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All right, so in this problem, we're looking at an airplane that is coming in for a landing. More looking at how long it takes it to clear an intersection. My clear. I mean, the tail of the plane is completely out of the intersection. So the pieces of information we know from the get go here is that the final velocity of the plane after it has cleared the intersection is 45 meters per second. While it is going through the intersection, it is accelerating at a rate of negative 5.7 meters per second squared. That negative value is showing the fact that the plane is slowing down as it is coming in for a landing and the distance the plane travel's is a little more complicated than normal. First up, the intersection itself is 25 meters, so when the head of the plane hits the intersection, it needs to clear that 25 meters. But the plane itself is 59.7 meters long, so once the head is out of the intersection, you then have to allow for the entire rest of the plane to travel through it, which is an additional 59.7 meters, meaning the plane actually has to travel a distance of 84.7 meters before none of it is left in the intersection. So our goal here is to figure out the time it takes for the plane to clear the intersection. In order to do that, we're gonna have to do it in two steps because we need to find that initial velocity before we can find the time. So Step one, let's find that initial velocity. And since we don't know the time yet, we're going to be using our equation. That does not have time in it, which is our 2nd 1 The V squared equals the not squared squared, plus two a X. Now I'm gonna rearrange this to solve for that X value or to solve for the V, not value. So we'll subtract the two X So I have b squared equals. I'm sorry that's be not squared equals V squared minus to a axe. And then because I want V not by itself, I will square root both sides so we get, be, not equals the square root of V squared minus to a X. When I plug. My number's in here. That gives us the square root of 45 squared. Um, plus 965.58 When I plug that into my calculator, I get my answer of initially The plane is traveling 54.7 meters per second when it hits the intersection. And then that number I can plug in with my known values up here, and we can use that to find the time it takes the plane to clear the intersection. So let's move my first chunk down here. And now I want to use an equation to determine the time. And since I know all the other components, we're gonna work with this first equation here to figure out the time So velocity equals V not plus a T. Since I'm looking for time, let's take a second to rearrange this one as well we get. The time is equal to the minus B not divided by the acceleration I plug my numbers in. That gives us 45 um minus 54.7 divided by negative 5.7, which gives us a final time of 1.7 seconds. So while this plane is coming in for a landing and slowing down the entire time. Some portion of the plane is in the intersection for 1.7 seconds total.

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