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. (b) Let x be east and y be north, and find the components of υ→ P/E.

Video transcript

Welcome back everybody. We are told that during aviation training we have a jet fighter that is traveling north and its air speed or the velocity of the jet relative to the air is 70 m/s. Now, while this is happening there is a strong storm that is subjecting the jet to a northeast wind. Now the velocity of this wind or air just moving represented by a relative to the Earth is equal to 27 m/s. Now we are tasked with finding the X and Y component of this vector. I just drew here in this vector of course, is the velocity of the plane relative to the earth. And we know by our little diagram here that the velocity of the plane relative to the earth is equal to the velocity of the plane or the jet relative to the air ak its airspeed plus the velocity of that gust of wind relative to the earth. So we are going to use this formula for both the X component of this vector and the Y component of this vector. So let's start off with the X component. Well, to find this, we're just going to sum up the X components of the other two vector. So let's start out with this, the X component of the air speed. Well, it's fully traveling in the y direction. There is no X opponent that's just going to be zero plus the X component of this velocity vector right here of this wind. Now, here's something important. We are told that this wind is traveling northeast, meaning that it is making a 45° angle with the vertical y axis so we can use that to our advantage. So if for this little X component right here we are going to have the magnitude of that vector where the velocity times the sine of our angle 45 degrees. And when you plug this into a calculator you get the X component is 19 point oh nine m per second. So let's go ahead and find the Y component in the same exact way the Y component of our vertical airspeed is going to be the entire vector itself, it's solely traveling in the Y direction. So this is just going to be 70 plus the Y component of our vector up here. This time it's going to be the magnitude times the co sign of our angle 45 degrees. Plugging this into our calculator, we get 89 point oh nine m per second, meaning that we have found both the X. Component and Y component of the velocity of our jets relative to the earth corresponding to answer choice. C Thank you guys so much for watching. Hope this video helped. We will see you all in the next one