1D Kinematics Legacy Problem #29 Guided Solution

You know, I've been teaching a number of years now, and I can't count the number of times that I've had a frustrated student come to me and just simply say, I can't do these problems. And in probing the nature of the problem, I typically get the response, I just don't even know where to start. I can't even begin the problem. And that's where these habits of an effective problem solver become so critical. Because in order to figure out how to solve a problem in situations like this, you need to have a strategy that you can consistently use, that will always work for you, that gives you confidence. When you get stuck, you can unstuck yourself. And that begins by careful reading and visualization of the problem, and writing down of information, maybe even diagramming the problem. Here what we're told is a military jet's taken off an aircraft carrier, and the way it generally works is a military jet needs to have a specific speed relative to the air in order to take off, or it just simply can't get the lift it needs to get up in the air. That's true of any plane. Now, in order to get that lift, you have to be traveling so fast relative to the air, so aircraft carriers have very short runways. And so what they have to do is they have to travel really fast into the wind. And if they're traveling really fast into the wind, they get a little extra boost from the fact that that little aircraft carrier and the aircraft on it are actually moving relatively to the wind, even though they're not moving relative to the boat, if you can picture that. So here we're given some information about two possible ways a military jet could take off. And in one case, it's taken off on a carrier that's traveling 45 miles per hour to a 20 mile per hour wind. And when that happens, it only needs to be traveling relative to the deck of the carrier, 45 meters per second. And what we wish to do is we wish to calculate the minimum acceleration it needs in order to take off to achieve this takeoff speed of 45 meters per second. So what we're going to list is, like for any jet, is that the jet is traveling zero meters per second originally relative to the aircraft carrier. V0 equals zero. And in this case, VF equals 45 meters per second. We're looking to calculate an A, that's our unknown, and the 126 meters is the distance that it has to take off. So that's the D, 126 meters. So what we're going to do is we're going to list those three knowns, the V0, the VF, and the D. We're going to look for an equation that has those three unknowns, those three knowns, and the one unknown, the A. The only equation of that nature is the one that goes VF squared equals V0 squared plus 2AD. Now, the V0 is zero, so that term cancels from the right side, and the equation simplifies to VF squared equals 2AD. Plug your 45 meters per second in for VF, set that equal to 2 times the unknown A times the known D of 126, and do your proper algebra, being careful to square the 45, and solve for your A. Now, the second part of the problem is just for a different set of conditions on the aircraft carrier and the wind. The aircraft carrier is now traveling in the wind 10 miles per hour into a 5 mile per hour wind, and so not as much of a boost from the carrier speed or the wind. So the aircraft needs to be traveling 71 meters per second with respect to the deck of the aircraft, with respect to the deck of the carrier. So what we need to do is repeat the calculations, but instead of using 45, use 71, and that gets you your answer.