The nose of an ultralight plane is pointed due south, and its airspeed indicator shows 35 m/s. The plane is in a 10–m/s wind blowing toward the southwest relative to the earth. (a) In a vector-addition diagram, show the relationship of υ→ P/E (the velocity of the plane relative to the earth) to the two given vectors.

Video transcript

Hi, everybody. Let's go. So during aviation training, a jet fighter is traveling due north, the pilot reads the S I or air speed indicator as 70 m per second. Unfortunately, the weather is considerably harsh and the jet is subjected to a strong wind blowing towards the northeast direction at a speed of 27 m per second. Which of the following vector edition diagram shows the correct relationship between V of J E the jet velocity relative to the earth and the two vectors. So we are given some variables here that we want to know. So we have a velocity of our plane, our our our our plane relative to sorry about that plane relative to the air. It's moving at 70 m/s. We also have a wind speed. The velocity of the air relative to the earth of 27 m/s due north east northeast is important because if we consider over here a compass with north east, south west, if we look at this, the way we would an xy graph, northeast being here Would form a 45° angle On that graph. So since our plane is moving directly north and we have a wind of the northeast, it should be hitting it at a 45 should be hitting the plane at a 45° angle. So we have our, so we have two vector values over here. And then we also have the angle of the wind. And now we need to find which of these graphs is going to show the correct relationship between these vectors and with the correct angle. So right off the bat, we can see that A is not going to be correct because it has A 30° angle that the wind is approaching at. And we know that's not right Here, we have a 45° angle. So that could be it Another 45 degree angle. And here we have a 30° angle. So D is not gonna be correct. So it's either gonna be B or C. So now let's look at our different vectors. So we can see and be here. It looks like the difference between B and C is that is the direction of the wind N B. We can see the vector of the wind is highlight that in blue, the vector of the wind is going this way towards the northeast, which is what we would expect. And in probably in answer, see the vector is heading northwest. So even though it's at the right angle, it appears to be going the wrong direction. So that just leaves us with answer B and that is going to be the correct graph. Thank you.