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(20 points) The salmon of Capistrano are migrating south to Aspen for the winter A wind blows from east to west at 16 mph: The salmon can fly at 22 mph through the ...

Question

(20 points) The salmon of Capistrano are migrating south to Aspen for the winter A wind blows from east to west at 16 mph: The salmon can fly at 22 mph through the air A) In which direction should the salmon fly through the air so0 that their net movement is directly south? B) What will be the salmon'$ speed over the ground, VsG, if they are in fact moving due south?VSA 22 mphVAG 16 mph1 .EAspen

(20 points) The salmon of Capistrano are migrating south to Aspen for the winter A wind blows from east to west at 16 mph: The salmon can fly at 22 mph through the air A) In which direction should the salmon fly through the air so0 that their net movement is directly south? B) What will be the salmon'$ speed over the ground, VsG, if they are in fact moving due south? VSA 22 mph VAG 16 mph 1 .E Aspen



Answers

Round your answers to two decimal places. A glider traveling at 90 miles per hour in the direction $\mathrm{N} 20^{\circ} \mathrm{W}$ encounters a mild wind with speed 15 miles per hour. If the wind is traveling from east to west, find the resulting speed of the glider and its direction.

So we're talking about planes and cross bins, which, of course, is a lot to do with Victor's. Before we start a problem with this, what we want to do is decide on a convention or how you want to talk about direction. And usually the convention is going to be that North is in the positive y direction, and East is in the positive x direction. Uh, this is this is the standard, um, invention that we usedto to talk about, um, things like this. Like a flight in a cross wind or maybe boats on the river, something like this. Um, and of course, with this, we would also notice that, uh, in the negative Z direction would be the downward or ground word direction to men in the positive Z direction. That would be upward or skyward. Um, so, yeah, we have to decide on this convention early and stick to it if we If we don't, we might run into trouble weight on the problem. But now that we've decided on our convention, we can go ahead with this problem. This problem is a model airplane that is flying's Oliver. This p for a plane. The Vector P is flying due north. So that zero in the east west direction uh, 20 in our north direction. Right. So we said North was positive, Ally. So we're flying 20 MPH north says dear 20 end, it is horizontal. Um, so in still air, this plane would be flying 20 MPH due north. But we also know that our air is not still we have wind that is blowing at 20 knots per hour due east Eso he said East was the positive extractions. We have 20 MPH in eastern direction and then zero north south, zero up, down. So this is our wind vector, which will be blowing 20 MPH due east. And then we also have a draft. In this case, it's a downdraft. We'll use D. And that's going to be, uh, vertical. Right? So there's no north south now east west component. But there is a down component, right? It's a negative 10 MPH downdraft. So these are all of the vectors we're dealing with, right? We have the plane moving at 20 MPH north. Um, but we also have a wind pushing it at 20 MPH east. And then we, uh, also have a downdraft pushing it, and it's gonna be hard to draw that perspective. Downdraft pushing it negative 10 MPH. Uh, ground word. So these are three components and were asked to find the velocity of the plane relative to the ground on that velocity is going to be the sum of all of these vectors, right? So if we rescind all these vectors, we would have the plane plus the wind plus the draft and we can see they gave us a pretty easy set of vectors to some here because our X component is going to be the 20 positive 20. Excuse me? There's gonna be positive 20 from our cross wind, or why component is gonna be positive 20 from our plane's flight and still air. And then rz is gonna be negative. 10 from the town draft. So this is the velocity of our plane relative to the ground. Sometimes that can be confusing because it sounds like this is the velocity of the plane. But this is the velocity of the plane relative to the air. Whenever they give you when you were doing with a question like this to give you the velocity they're playing, They're talking about the velocity of the plane relative to the air. Um, and we also know that the air is moving relative to the ground. So in order to find the plane relative to the ground, we have to add plain relative to the air with the air relative to the ground. I've been doing that. We get plain relative to ground, which is the sum of all three of these. So until we get that this 2020 negative 10 is the velocity of the plane relative to the ground. Um, but we could go a little bit further if we wanted to find the speed of the plane relative to the ground. Well, room the speed is, um, the magnitude of our velocity. So because of this the and if I want to find the magnitude of the which is our speed on TV, that's going to the square root of each of these components squared, it's going to score 20 squared less 20 squared, plus negative 10 squared, which equals the square root of 900. And we know that the square to 100 is just 30. So there we have it. We found the speed. This is gonna be a master. Our the speed of our plane relative to the ground is 30 MPH. Um, the and we could describe its velocity in terms of this vector 2020 negative 10.

We know that the velocity of the eagle relative to the ground he's going to be equal to the velocity of the equal of the equal relative to the air, plus the velocity of the air relative to the ground. Now we know that the velocity of the air relative to the ground is going to be equal to 35 miles per hour, and we're choosing. We're choosing east to be positive. So East is positive. So essentially, Ah, for part a, the velocity of the eagle relative to the ground would be equal to 22 plus 35. This would equal 57 miles per hour. However, this would only occur if the bird I was flying west to east and then for part B the velocity of the eagle relative to the ground would be equal to 20 would rather be equal to negative 22 plus 35. So this would be equal to 13 miles per hour, and this would be again Byrd flying east to west. That is the end of the solution. Thank you for watching

In discussion. It has given that an airplane is flying At 325 mph and still air And the spirit of the tailwind is 40 mph. So let's write velocity of airplane is equals two, 325 MPH and the velocity of wind. Air is 40 mph. It has given that the direction of the airplane is 20 degree east to north and the direction of the taliban is 40 degrees west to north. Here the compass heading is maintained but due to wind, airplane acquires a new ground speed and direction. We are required to find this new ground spirit and direction. So let's see how to solve discussion. First of all, let's calculate the angle made by the airplane with yeah positive X. X. Is is and this will be 90 degree minus 20°. He recalls to 70 degree. We know that the component form of a vector is X. Comma Y. Where extra pickles too. On course I intend to and why the calls to our scientist to Yeah, therefore the component form of director of airplane velocity will be X. Come away if he calls to 325 Claussen 70 degree coma. 325. Sign 70 degrees. So many for the calculate this, we get the component form of the velocity vector of airplane that is 111 point 157 comma 305 400. And now let's calculate the angle made by the ale wind with mhm positive X. Access is given by AL five calls to 90°. So this will vehicles to 100 and 30 degree. Therefore the component form of the bill, wind velocity will be 40. Yeah. Co sign 130 degree coma 40 sign 130 degree. So many for the calculator. This we get minus 25.712. Coma. 30 point 642. Yeah. No. We know that if a vector U is represented by you one comma you too. And another factor we is represented by we even coma V two. Then the resultant vector or the sum of U plus V. Can readiness? You won plus v even comma you two plus we do. Therefore the alternative actor will be close to 111.157 plus -25.712, coma 305 point 400 plus 30 point 642. So this will be close to 85 point Yeah. 445 comma 336 point zero for two. And we know that the magnitude mm hmm. Of a vector a coma B is given by magnitude a comma B equals two. And the root of a squared plus b squared Therefore the magnitude of 85.445 comma 336.042 will be calls to under root of 85.445 to the power to plus 336.042 to the power to. And when you for the calculator. This finally we get 300 and 46 seven 35 miles power. And we know that D direction angle tita is Given by three testicles too. Tangent inverse be upon A. Here B is the 336.042 and a is 85.445. Therefore, data will be close to tangent inverse. 336.042, divided by 85 point 445. So many for the calculator. This finally we get keita recalls to 1.321. It east to North hands. We can't include that. The airplanes. New Spirit is 346 735 MPH. And it's a new direction is mm 1.3218 east to north. So this is a final answer for this problem. I hope you know for the solution. Thank you

So for this problem we're dealing with a wind velocity of 45 miles an hour, that's blowing 20 degrees west of North. So it's blowing about, we could say this is the the wind back to right here. And I'm an airplane is flying at 425 miles an hour. Ah Yeah, in still air is supposed to be flying straight north, so like this, but we know the wind is pushing it this way. So we want to know how the plane, how should the plane be headed and how fast it will be flying with respect to the ground? So we know that if we find um this vector right here, the one that is formed from their parallelogram, that will tell us how fast and how what direction it would be traveling in. And that would be that it's going slightly um slightly faster because it's pushing it up, so it's gonna be 467 miles an hour. However, it is going to be pushing it slightly off track somewhere in between zero and 20 degrees west of North


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