An airplane pilot wishes to fly due west. A wind of 80.0 km/h (about 50 mi/h) is blowing toward the south. (b) What is the speed of the plane over the ground? Draw a vector diagram

Question

Accepted Answer

Hey, everyone in this problem, the pilot of a trainer plane wants to travel due east. Ok. A wing that is classified as a storm by the weather station blows towards the north at a speed of 100 kilometers per hour. The air speed of the plane is 300 kilometers per hour and instill air. And we're asked to calculate the speed of the trainer plane over the ground. And we're told to draw a vector diagram to help us solve the. Now we're given four answer choices all in kilometers per hour. Option. A 339.1. Option B 265.3 option C 315.4 and option D 282.8. All right. So let's start by drawing this vector diver. Now, what we want is the plane that wants to travel to east. And what that means is that the speed or velocity of the plane with respect to the ground should be directly east. Ok. So we're gonna draw that first. Ok. We're gonna say that east is pointing to the right and this is gonna be the velocity of the plane with respect to the ground. And that's what we want to find. Now, what else do we have? Well, we have a wind speed and the wind is blowing north at a speed of 100 kilometers per hour. We have this wind that's blowing 100 kilometers per hour. And this is gonna be this velocity or the speed of the wind with respect to the ground. And finally, we have the speed of the plane with respect to the wind. And we're told that that is 300 kilometers. Now, the combination of the plane traveling with respect to the wind and the wind pushing it is gonna give us this velocity or the speed that we want. OK, the velocity or speed of the plane with respect to the ground. So this is gonna form a little triangle where you can imagine if we add tip to tail with our speed of the plane with respect to the wind being 300 kilometers per hour. And we add this tip to tail with our wind vector and we get the resulting speed of the plane with respect to the ground that is going to east just like we want. All right. So now if we want to calculate the speed, we can do that. And we have a right triangle, we know two of the sides. We can use Pythagorean theorem. So the hypotenuse of our triangle which is 300 kilometers per hour, all squared is going to be equal to the sum of the squares of the other two sides. So we get 100 kilometers per hour square plus the speed of the plane with respect to the ground squid. Expanding what we have on the left hand side, we get 90,000 kilometer square per hour square. On the right hand side, we have 10,000 kilometers squared per hour squid. What the speed of the plane with respect to the ground square case of tracking 10,000 kilometers squared per hour squared from both sides be it that the velocity of the plane with respect to the ground squared must be equal to 80,000 kilometers squared per hour squared. And finally taking the square route to get that final speed that we are looking for, we get the speed of the plane with respect to the ground is going to be about 282.843 kilometers per and that is exactly what we were looking for. And it makes sense. It's a little bit less than the speed in still air because that wind is pushing against that plane and impacting its speed in the direction it wants to go. All right, comparing to our answer choices, we can see that this is going to correspond with answer choice D rounding to four significant digits. We have 282.8 kilometers per hour. Thanks everyone for watching. I hope this video helped see you in the next one.

An airplane pilot wishes to fly due west. A wind of 80.0 km/h (about 50 mi/h) is blowing toward the south. (b) What is the speed of the plane over the ground? Draw a vector diagram

Verified Solution

Key Concepts

Vector Addition

Resultant Velocity

Pythagorean Theorem