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In the following exercises, solve the given maximum and minimum problems.Computer simulation shows that the drag $F$ (in $\mathrm{N}$ ) on a certain airplane is $F=0.00500 v^{2}+3.00 \times 10^{8} / v^{2},$ where $v$ is the velocity (in $\mathrm{km} / \mathrm{h}$ ) of the plane. For what velocity is the drag the least?

Calculus 1 / AB

Chapter 24

Applications of the Derivative

Section 7

Applied Maximum and Minimum Problems

Derivatives

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Okay, This family, they say that we wanted to calculate minimum run railings or an airplane with using airplanes acceleration and take off speed. Eso There's going to be a three step program for when things first. ISS. Let's see from user for input. Yes, we'll use the consul is counsel and we're going through never toe convert steering input and the numbers to do calculations. And then we're going to calculate we minimum run railings We're gonna use the formula. They've given us length for the equal to, Let's see, be take off speed So right, speed squared Then we're going to you divided by yeah times the acceleration And then the third step we're going to display output Teoh user This case we're going to use Consul And remember Teoh convert two strings but in the opposite of what we did taken inputs right? Let's see, they give us an example when we prompt the user we're going to need to get pliancy speed on acceleration We're going to even see to turn our string input into numbers that we can calculate with we're going to ask for in print Let's see asunder speed and acceleration and it looks like the user is just gonna have to know that they should call on separate there. Okay, so we've run that at that point, and I were going to calculate it. Uh, I have to say that links going to be equal to, well, im formula taking it. It was like a power under going to divide 0.2 times the acceleration that we got. How are we going to display that to the using? Well, from their output, we congratulate into the conflict. Bring us A. The minimum runway link for this airplane is and they're going to give the number. They calculated our length, but remember when he had turned it into a string here? Right. So who knows how to combine a bunch of strings Or else it wouldn't know how to combine our string message on the number very easily. Then let's see you give that number and they make sure they let them know that they converted it. This they're probably didn't even ask the user and let them know the units. That's a bit interesting. You should always let them know. So let's actually improve on what they showed us. Let's say we want in the speed and me. There's for a second. And let's say that we want the acceleration in meters per second squared. Yeah, violence maps their input and see if we get the same out. But when they put it in, they put in for their test 60. Um, I agree with the comment three point by over the acceleration. So it's in that, and they end up with that. See, the minimum run away for the airplane is 5.1, important to eight and Aaron six. Okay.

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