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Of 13AttemiAn unsuspecting bird coasting along in an easterly direction 1,O0 mph when strong wind from the south imparts constant accel leration of 500 ms? . If the...

Question

Of 13AttemiAn unsuspecting bird coasting along in an easterly direction 1,O0 mph when strong wind from the south imparts constant accel leration of 500 ms? . If the wind $ acceleration lasts for find the - magnitude and direction (measured counterclockwise from the easterly direction) of the bird'$ displacement over this time interval. Assume that the bird is originally travelling in the +x direction and that there are 609 m inE6[[86Z0L'[29.22062587Now; assume the same bird moving alon

of 13 Attemi An unsuspecting bird coasting along in an easterly direction 1,O0 mph when strong wind from the south imparts constant accel leration of 500 ms? . If the wind $ acceleration lasts for find the - magnitude and direction (measured counterclockwise from the easterly direction) of the bird'$ displacement over this time interval. Assume that the bird is originally travelling in the +x direction and that there are 609 m in E6[[86Z0L'[ 29.22062587 Now; assume the same bird moving along "gain (O) mph easterly direction, but this time , the acceleration given by the wind is at 0 $ 38.0" angle t0 the original direction of mcxion, measured counterclockwise from the easterly direction, magnitude of the acceleration OO) ns? , find the displacement Vector {d the ungle of the displacement 0 = Enter the components of the vector; 41 puu ad the angle; Asume (he time interval still J0 $ Tyj 1.571699641 MacBaok Pr



Answers

With the same airspeed as in Problem $1.16$, in what direction must the plane head in order to move due east relative to the Earth? The sum of the plane's velocity through the air and the velocity of the wind will be the resultant velocity of the plane relative to the Earth. This is shown in the vector diagram in Fig. $1-19 .$ Notice that, as required, the resultant velocity is eastward. Keeping in mind that the wind speed is given to two significant figures, it is seen that $\sin \theta=(90 \mathrm{~km} / \mathrm{h})(500 \mathrm{~km} / \mathrm{h})$, from which $\theta=10^{\circ}$. The plane should head $10^{\circ}$ north of east if it is to move eastward relative to the Earth. To find the plane's eastward speed, we note in the figure that $U_{\mathrm{PG}}$ $=(500 \mathrm{~km} / \mathrm{h}) \cos \theta=4.9 \times 10^{5} \mathrm{~m} / \mathrm{h}$

Hi. So in this question, we have That plane is moving eastward at 500 km below and then the wind, It's common south at 1990 km/h. So the result on to be somewhere. So it's this direction and to find the result of vision. And use the pythagorean theorem. What you mean? So we have to have a triangle like this and they should set a little for this is 19. That's right, uncle here. So resultant scored as we that'd be my chief squared 500 squared squared, Just be cool to 508 kilometers per hour. So as for the direction and speed related to the ground, we're going to take his turn. They don't equal to turn in the US of the critical over the region. Jimmy 90 Run it by 500. Yes, we can call to approximately 10 degrees. Okay, So 90° was here, You know, 500 this year. So I'm gonna be 10 degrees In between the two victor's And I blew the hard on top 10° to 10 degrees south of East, trump both east

In this situation we have given the coordinates of world flying in xy plane and we have to find the part of the birds between time. T is equal to zero seconds two seconds and velocity. And the acceleration rectors of this bird. So first of all we have given that. Yeah. Yeah right. Ex coordinated you owned by the extreme supposed to al fatty and we have you on the Y coordinate that. It's quite easy. It was to three minutes better. T. Square. Now we have learned the value of alpha area that is 2.4 m per second. And we have beyond the value of data. That is 1.2 m/s square. No first part we are to the sketch we can see that for I am that is physical 20 2nd x is given by dirties zero and Why will come out to be three and for time to use equals to two seconds. The value of acting by will be that is Exit to his witness that is two times of alpha and this will come out to between 2 2.4 that is four eight m. And we can say that why is given by that is three minus This is the time to and this will come out to be minus of 1.8 m. Now I'm going to sketch the graph of the solution so we can say that let this is our Y axis and this is our X axis and let this is the Time physicals to zero and this is that so and this is X equals to zero. We can say our I will be when X is zero the value of Y is three. So why is there tree and access when 4.8 Sorry, when time is too the value is a negative negative minus of 1.8. So the graph will become like this and this is slightly curled so this is our graph for distribution. Now we have to find the acceleration and velocity so we can see that we're nothing director is given by dirties. We were pretty close to X. I get less of my jacket. Sorry disease. Mm We know that velocity actually is given by dirties. Bx upon dating I kept plus divide by DT of Jacob. So this is ALF I get muscle to be trying to teach Jacob. Now put the value of alpine because so this is 2.4 of I kept so This is -4.8 of Jk. Now I'm going to show the diagram. So this is deep, 2.4 I kept in extraction and this is -4.8. So this is in minus direction. So this is the value of 4.8 in J k f. So this is our resultant let this is angle to it or not. So we can see that the magnitude is given by that is And the root of 2.4 square plus minus of 4.80 square and this will comes out will be 5.37 m/s. So this is the value of is speed. And the angle can be found that is 10 to to know what is given by -4.8 upon This is 2.4 and this will comes out to be a teacher, not a year minus of 63.44 degrees. Or I can say this is 3 16 minus 63.44. So this is 2 96.56 degree. So this is the angle, this angle is To 96.56 degree. Now we have to find the acceleration. So we can say that our velocity will be mhm that is 5.37 m/s At angle of 2 96.96 degree. This is the answer for velocity and for exploration we can say that this is the owned by that is a better Isaac was to debut by detail. So this all comes out to be- of two bitter Jk or and this will be minus of 2.4 of Jacob. This is the acceleration. We can clearly see that there is only this is the only Why direction. So this is our exploration. This is in Jacob direction though in the value of 2.4 soil magnitude of exhibition can be found by that is under oath of minus 2.4 Holy square. So this bill comes out to be 2.4 m/s squared. So this is the expiration and this is in downward direction. No, we have to find in the next problem that we have to show that is the body is speeding up or slowing down or it's a speed instantaneous, not changing. So we can clearly say that it is, our expectation is in downward direction. So we can see that it's expiration is in y direction that is downward and velocity component is also in right direction, so bird then it's cleared up. So this is our answer for this part of the problem in this bird will dispute up and it will turn to watch minus by direction. This is actually negative direction, downward direction. So this is I want to answer for this given fusion. Thank you.

So this problem wants us to the turning to velocity of the wind with respect to the ground and determine the angle relative to to stop. So this is the, let's notice as we sub G, which is the velocity of air relative to the ground. So we know that my relative velocity, the velocity of the plane relative to the ground is equal to the better some of the velocity of the plane. The small aircraft relative to the wind, which is the air plus the velocity of the air relative to the ground, which is what we're looking for. So rearranging velocity of the wind relative to the ground is the vector difference of velocity of the plane relative to the ground and the velocity of the plane relative to the air. So we have to find first for your horizontal and vertical components to get magnitude, since we know that the magnitude it was to discredit off that some of the squared of horizontal and vertical components, we have the A G X, last V a G What square then? For V a g G X. Because to D p G x minus B B A X. So we have For the velocity of the plane relative to the ground. It stated that for 900 seconds the distance traveled this 81 1000 m at an angle of 45° which is restive south. So we have since ways of south, so negative 81 km. so 51,000 m Over nine times 10 days to two seconds or 900 seconds, Multiplied by sign 45°. She's good. My nose. The mhm, horizontal component of the velocity the plane relative to the air to the wind. And since the plane is perfectly vertical it is drew south, it does no horizontal component. So this is zero. So And the answer is the horizontal component of the velocity of the wind relative to the ground is negative 63.64 m/s. Not for the critical component. Okay, we have it's also negative as well since ways of south Over nine and a second multiplied by close to 45° -2.8 m/s, which is the velocity of the playing relative to the air. And it is negative since true to south. So so that you can find us. This is equal to negative 5.84 m/s. So now getting their magnitude then we have -63.64 m/s Squared plus negative 5.84 m/s. It's Greg, mm hmm. The z equals two 63 .9m/s. So this is the velocity of the wind relative to the ground. So now for the directional angle, if it's red. If the problem want us to express her lesson relative to do to sound, then the opposite side is the horizontal component. So we have the A. G. X. In the gaze inside is the critical point. So the egg what getting better budget numbers of their absolute value? And we have negative 63.64 meter per second over negative 5.84 m per second, getting the tangent inverse of its absolute value, then the secrets to 85 degrees. And since the horizontal component is negative in the critical component is also negative, then the direction is west of stop. Mhm.

Higher. Priven. Here it is. Given the coordinates off. Word flying in the X Y plane are given by X Coordinate is given. Find duty on Dwight Gordon. It is given 3 m my nets. We teach quick there and for having that who pile 4 m per ticket on beater. Having the 1.0, meet up our second square in the party Be upto sketch the but off the word foot Do you know toe ticket and be part we have to find velocity I acceleration. Defunct enough, right? And see part magnitude under the addiction Oh, velocity and acceleration at Pete's call to ticket drop velocity, bra, velocity and acceleration back to at peach cultural music It on defined its image. It post by We have to sketch the part Toby. Certain know the value of action bite so But first we will find the value of action. Bite for a given time. Interpret exit measured by I'll find duty on l pies to find puts it directly. I can right here. 2.4 in 30 on bike and greediness Do You might miss 1.2 into p square. This will be in meter This is meter diamond sick and doodle Expel video bible with perimeter for excess Beethoven authorities Cult one X ability. 2.4 m and bite is 1.8 m for peace. Call to second exit vehicles for quite admitted and by becomes a minus 1.8 m. Now you can put the grab between X and bite access taken along the original direction. 0 m, 1 m. We'll meet that. Did you meet that yet? One through. Okay. Minus one minus two. No blood. Aggio. Why is given Dr Three access zero. So the draft will be like this one. So city it is in meat. It This is God's doing meted. So grab will be like this. Let me correct, little bitch Because we are plotting in free and and this will be foot. So this is the interrupt first part now in ticket. But Felicity velocity XX is okay, b It's up on duty. So it would meet l for on velocity alone by exists devalue quantity Who will be judging acceleration and extra action The the X up on duty. So it is, you know, because and by its constant acceleration along by exists that is minus two bitter so velocity of after candidate in its B X I kept blessed be by pick up So this is the velocity vector as a function off type on acceleration Back trilogy function of time Do you delight Cap minus 2 m dick up So this is the answer up be I see after he started to you know So the activities canto ticket but a city Yudof X axis and only on al fights given to point foot velocity along by exists minus two And don't beater That is 1.0, used to take it It will be minus four white it meter per second So velocity you will get the excess quick But I would be very square that is 2.4 Holy Square Validity having the manager five point food meters per second on its a direction And for Dannon what's up? Be very upon be it's minus four Quite it upon who point for that you will get minus 63.4 degrees You can draw the Bagram That's it. X component off Felicity this is my component of validity. This is the velocity on this angle is give it no acceleration. Acceleration is to find it. E x. I kept Let's ive by Jacob Extracts and acceleration is zero by direction. It is minus two bitter Vitale's been point to minus 2.4 meters per second squared Jacob. So here it's the magnitude is you don't minus 2.4 Holy square, that is 2.4 m per second squared and it's directs and l fights called to 10 in Warsaw minus 2.4 upon Jiro that is minus infinity. So it would be in this medics b but be a good drop. Well, the city back and exploration vectored velocity is in this direction already. Be up, major. You can result this little validity on perpendicular to validity. Food having the component along. But it's a D vector, so validity is increasing. Second, the acceleration having component perpendicular to Felicity. So it's the direction is also changing. So good spirited, increasing andare. Excellent ending. Thanks for watching it


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