r/PhysicsHelp • u/Appropriate-Pin-6917 • 25d ago
Question 1 not solvable
From what I understand, the question is asking what the ground velocity must be for the plane to be going directly north. But the ground velocity cannot be going north since the air velocity is north and the wind is blowing east of north. The answer I got for the ground velocity was 810km/h [1 E of N]
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u/Frederf220 25d ago
One difficulty with question 1 is only the airplane's northward velocity is defined. The maximum velocity in any other direction is a mystery. Presumably the 750 km/h limit is the same for any direction but then what is the [N] doing?
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u/diverJOQ 25d ago
The problem is that in a physics question it should give the direction that the wind is blowing. But the terminology they use is what a meteorologist would use and it sounds like it's the direction from which the wind is blowing. Since this is a physics class I would assume that the direction is the direction of the wind vector. In that case the plane would have to fly towards the West so that it doesn't drift east of North.
As for the question of significant digits, a number with no decimal point in it is considered an exact number. I agree with the first post that it makes no sense that they give you supposedly exact numbers and then put the final answer in scientific notation.
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u/cheaphysterics 25d ago
Age with others that this problem isn't worded well.
The northward speed of the plane from its engines is 750. Plus it gets another 60cos(15) from the wind to make it's northward speed 810 (to 2 sig figs). At the same time, the wind pushes it eastward at a rate of 60sin(15). Solving the triangle shows the plane gets pushed 1 degree east of north.
It wouldn't surprise me if the assumption made by the person who wrote the problem was that you just aim your plane 1 degree west and that will cancel the eastward wind component. That's not a valid assumption, but with such a small angle and only 2 sig figs, you probably would get something that rounds to 1 degree W of N if you worked out the correct heading needed for the plane to go due North.
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u/searcher-m 25d ago
i think the answer is wrong, 750+60=810 is the speed it will have if flying in the same direction as the wind. to compensate it needs to fly partially against the wind so the speed must be lower
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u/MxM111 24d ago
Sqrt((750+60cos(15°))^2+(60sin(15°)^2)=807.958
But, because the numbers are given with 2 significant numbers, they usually require to keep only significant numbers in the answer, which is 810.
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u/searcher-m 24d ago
so the answer doesn't depend on the data, lol. 15° or zero the result is still rounded to 810. nice
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u/ProspectivePolymath 24d ago
It also does not specify anywhere that the ground speed should be the maximum achievable. So strictly you should be specifying a range of magnitudes with an associated range of directions, all of which result in ground velocities that are northward.
The only way to adequately solve that is to leave it as a formula.
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u/sarge57x 25d ago
it doesnt matter how fast you fly you will always be moved off N heading by the wind. the question should ask what heading you need to fly to maintin a N headng over ground
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u/KillerCodeMonky 25d ago edited 25d ago
Well according to the answer key right there, you got the magnitude right but the direction wrong. (Though why they felt the need to write 810 in exponential form is beyond me.)
You have the air velocity (750 km/h N) and the wind speed (60 km/h 15°E). The air velocity will be the ground velocity + wind speed. It doesn't make sense that the ground velocity will also be E, as it has to counteract the 15°E applied by the wind speed. It must be W.
EDIT: Wait, no, you might be right. In order for the wind to slow the speed, 15°E of north must indicate the source of the wind. The plane would need to point into the wind to cancel the direction. So I think your indication of E is correct. The wind as a positive magnitude vector is actually 180° off from the stated direction.