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For the situation described in Problem 4,A 100-meter dash is run on a track in the direction of the vector v = 27+5j_ The wind velocity is w= 47 + j mph_ The rules ...

Question

For the situation described in Problem 4,A 100-meter dash is run on a track in the direction of the vector v = 27+5j_ The wind velocity is w= 47 + j mph_ The rules say that a legal wind speed measured in the direction of the dash must not exceed 3 mphfind the wind velocity vector in the direction of # = 47 + J so that the wind speed in the direction of Ihe dash is equal t0 3 mph: Make_sure_YOLexplain YOULwork'

For the situation described in Problem 4, A 100-meter dash is run on a track in the direction of the vector v = 27+5j_ The wind velocity is w= 47 + j mph_ The rules say that a legal wind speed measured in the direction of the dash must not exceed 3 mph find the wind velocity vector in the direction of # = 47 + J so that the wind speed in the direction of Ihe dash is equal t0 3 mph: Make_sure_YOLexplain YOULwork'



Answers

A plane flying due east at 200 $\mathrm{km}$ h encounters a $40-\mathrm{km}$ h wind blowing in the north-east direction. The resultant velocity of the plane is the vector sum $\mathrm{v}=\mathrm{v}_{1}+\mathrm{v}_{2},$ where $\mathrm{v}_{1}$ is the velocity vector of the plane and $v_{2}$ is the velocity vector of the wind (Figure 29$) .$ The angle between $v_{1}$ and $v_{2}$ is $\frac{\pi}{4}$ . Determine the resultant speed of the plane (the length of the vector v).

We have a question in which we need to uh we did uh from the chapter of vectors. Okay, so we have to just add these two vectors. We were and we do to get the resultant vector. We, because we need to find the result in the speed of the plane. This is the speed of the plane and it has started flying and they say the speed of the wind. So insulting. The speed will be V. So and uh we have t to cool to buy by four V one and V two are being given. This is very even and this is V two. So from the love edition of vectors, We'll be having vehicle to even Squire plus we to esquire plus two. We won. We too cause theater where theta is the angle between Vienna and veto. Okay, so we will be called to 200 square plus 40 sq Place two and 2 200 to 14 to caused by before. So we have to use can make up for this The 200 square place for Peace Square Plus two into 202 40 and two caused by the fall under the scheduled. So this is 200 30.0-9, so result in the speed of the airplane approximately will be 230 kilometers para. Thank you so much.

All right, we've got a question about someone running 100 m dash on a track in the direction of the vector V equals to two. I waas six check, all right. And we're told that the wind velocity it's equal to five. I loss she to jail kilometers per hour. And we're told that the rules were saying that the legal wind speed is measured in the direction of the dash must not exceed five kilometers per hour. Well, when they were asked to answer, what was the race results be disqualified due to an illegal went So essentially, I guess in order to make the race fair, they've set certain rules in place to ensure that the wind does not become a substantial factor and influence in the race. And they've deemed that to be the speed of five kilometers per hour. All right, so basically what we need to do here is just solve for the speed of the wind. If we consult for the speed of the wind and then we can see if it's greater than a less than five kilometers per hour and we'll know whether or not it pulled a substantial, uh, factor in determining whether or not this race is to be disqualified or not. Okay, so whenever we're solving for the speed or the velocity when were given a vector, we take the dark products and we divide that by the magnitude. Eso you do You gotta be over. Um, the magnitude Okay. In this case, are you is going to be our wind. Okay, so our w dot be over the magnitude our be here, which would be to I for six years and basically replicating the the equation. Just my attitude. Okay, Now the answer here will be you have five times two just 10 and then 10 plus 12. So we have at the top 22. Take the dog product and then the magnitude here would be square root of two squared plus six square No. Two squared is 46 squared is 36 four plus 36 is fourth, right? And then you go ahead and plug this in into your handy dandy calculator. We'll get the answer. 3.4 eight. We can see that 3.48 kilometers per hour is clearly not greater than five kilometers power. So we can confirm that the wind will not be a substantial factor in the race. Therefore, the race, the race results its salts stand this so they stand perfectly fine and the race is not this horrible or the race results. Excuse me, are not going to be this world or in in order to solve this question just to clarify We took the window back during the philosophy that term we need to find speeds. We went ahead and, um took the dot product over the magnitude led to our speed and they found that it was less than five kilometers per hour. Therefore, race results stand and the race results were not disclosed. I hope that clarifies the question. Thank you so much for watching.

This question asked us to find the speed of the wind writing out our equation. What we know we can first off do as we can cross multiply. This is gonna be an effective way of writing. Are factors in distribution form so we can distribute. When we distribute. We have, Yeah, we have 180 s is 7200 which means our ass is equivalent to 40 and the speed of the wind would be miles per hour.

Hello there. Okay so for this exercise ah we have two velocities in this case the first velocity is the velocity of the wind. That's denoted by the one And it's 40 mph then. And also we have the direction that is moving from east to west. And the hair plane that travels would here Of a speed with two that is 100 mph and its duty in art. Okay. So the speed of the airplane relative to the ground, it's going to be some of this vector. And the first thing that we need to do, well it's just calculate this vector. Okay so we need to give some directions to this vectors. So be one, it's going to be equal to 40 mph and going to move from east to west. Okay, that means mine is either okay we're going to consider following system. So north east west and south. So technically jay in the J direction will be the north to the I direction will be the west. And so one to the east. Well the point in the picture, so if we're we're moving from east to west basically that means that minus I'd. Component for the vector B. One. Now for the victory batou that corresponds to the hair plane, The speed of the airplane will be 100 miles and it's moving to the North. So it's going to be J. Okay so then we need to obtain this the the vector of relative motion. So let's call it just Beat. It's equals two B 1 plus b. two. It's going to be equal to be one, blessed be too. It equals to the victor minus 45 plus 100 jay. And we need to draw a figure. Okay, just kale. Okay, so basically the figure will be more less like this. Here have the excuse. Nice. So first you're going to have this victor, The one that's moving 4 -40 To the -1. Direction, so this -40. And then you have the move of the hair plane is going to be this victor. B two is 100 mph to the north. And the result in the vector that which is obtained it is this vector here, the that is the sum of these two factors.


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