For the second part:
The draw the plane vector which is the same as the desired results. At the end of the plane vector, draw the wind vector. That is where the plane will end up. So, for a 1/2 hour flight:
(80 km/h) * (hour/2) at 30 degrees E of S.
or 40km at 30 degrees E of S of the desired destination.
I don't understand the diagram. Can you please explain? I also don't understand why you used the wind velocity.
OK, here is what was stated for the continuation of the problem. I called this the second part.
"Suppose the pilot disregarded the wind and had flown in a direction of 30 degrees N of E. Where relative to his destination would he be when he thought he should be at the destination?"
Since the pilot is disregarding the wind, the plane would be flying at 30 degrees N of E. at 400km/h. But, since the wind is acting on the plane it will blow it off course. It would get to the destination OK if there was no wind.
Remember that the pilot is hoping to get to the destination which is 200km away in 0.5 hours.
First draw distance vector for the plane. It will be 200km at 30 N of E.
From the end of that vector (which actually ends at the hoped for destination) draw the distance due to the wind vector. That will be 40km (remember that this is a 1/2 hour trip). The wind drift will be in the same direction as the wind which will be 30 degrees E of S.
Thank you so much! I understand it now. With these problems I'm having a hard time deciphering the question.
Certainly! In the given scenario, we have a plane flying at a speed of 80 km/h for a duration of 1/2 hour (30 minutes). To determine the final position of the plane, we need to consider two vectors: the plane vector, which represents the distance and direction the plane would travel if there were no wind, and the wind vector, which represents the speed and direction of the wind.
To draw the plane vector, start by drawing a line segment in the desired direction of travel, in this case, 30 degrees east of south. The length of this line segment should be proportional to the speed of the plane (80 km/h). So, for a 1/2 hour flight, the length of the plane vector would be (80 km/h) * (1/2 hour) = 40 km.
Now, to incorporate the effect of the wind on the plane's movement, draw another line segment starting from the end point of the plane vector, which represents the wind vector. The length of the wind vector should be proportional to the speed of the wind.
By analyzing the diagram, you can determine the final position of the plane, which is where the wind vector ends. In this case, it would be 40 km at 30 degrees east of south from the desired destination.
As for why we use the wind velocity, it is because the wind affects the plane's movement. The wind vector shows how the wind will push the plane off its intended course. By incorporating both the plane vector and the wind vector, we can determine the actual path of the plane, accounting for the influence of the wind.
I hope this explanation helps clarify the diagram and the use of the wind velocity! Let me know if you have any further questions.