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Physics
a plane flying due north at 100 m/s is blown by a 50 m/s strong wind due east. what is the plane's resultant velocity?
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Here's the thing - that answer is wrong.
The magnitude of the velocity is given by pythagoras
SQRT{(100^2) + (50^2)} = SQRT{12500} = 111.8.
Round that to the nearest integer and it is 112 (not 110 as given in the answersheet)
The direction is due north pushed to the West by arctan (0.5).
Arctan (0.5) = 26.6°
so the direction is 26.6° west of due north. In bearing terms, that is either -26.6° or 333.4°
For some reason the answersheet has added the 26.6° to 90°
Weird, that.
The magnitude of the velocity is given by pythagoras
SQRT{(100^2) + (50^2)} = SQRT{12500} = 111.8.
Round that to the nearest integer and it is 112 (not 110 as given in the answersheet)
The direction is due north pushed to the West by arctan (0.5).
Arctan (0.5) = 26.6°
so the direction is 26.6° west of due north. In bearing terms, that is either -26.6° or 333.4°
For some reason the answersheet has added the 26.6° to 90°
Weird, that.
I guess maybe it's been rounded to 2sf, which is a little weird but whatever.
Also I wonder if the bearing in the link above is defined as "bearing from due East" (and with a wind that in that case was blowing west rather than east), which would explain the + 90 degrees.
Unusual conventions, anyway. But Kidas' answer is anyway complete and describes the general method.
Also I wonder if the bearing in the link above is defined as "bearing from due East" (and with a wind that in that case was blowing west rather than east), which would explain the + 90 degrees.
Unusual conventions, anyway. But Kidas' answer is anyway complete and describes the general method.
Thanks for reminding the maths teachers here about that, Kidas.
My excuse is that it's over a quarter of a century since I taught maths and my old grey cells aren't what they used to be. (I detested the applied stuff anyway. To me, maths should be a pure art form). I wonder what Fiction-Factory's excuse is?
;-)
My excuse is that it's over a quarter of a century since I taught maths and my old grey cells aren't what they used to be. (I detested the applied stuff anyway. To me, maths should be a pure art form). I wonder what Fiction-Factory's excuse is?
;-)
There is insufficient information in the question to determine the correct answer.
The unknown variable in the way the question is posed is what effect (force) the 50m/s easterly wind is having on the aircraft. If the aircraft is very streamlined at 90 degrees to its normal forward travel, the effect of the side wind will be minimal – but if the aircraft has a large fixed sail such that the major surface is facing into the wind, its direction will be very different.
The unknown variable in the way the question is posed is what effect (force) the 50m/s easterly wind is having on the aircraft. If the aircraft is very streamlined at 90 degrees to its normal forward travel, the effect of the side wind will be minimal – but if the aircraft has a large fixed sail such that the major surface is facing into the wind, its direction will be very different.
Oooh! Oooh! Exciting - can we get all geeky over a 3rd form homework question...
Because it depends on whether this is steady-state or a transient.
The jet engines are thrusting forward, not sideways. So there is no resisting force against the lateral wind.
If the wind has just started, Hymie is spot on - the plane will be accelerating gradually in the direction of the wind, and we don't know the forces on it, so we don't know how far it travels with the wind. It's a transient - that is to say the situation is adjusting to a new situation.
After a while, the wind has pushed on the plane (laterally) and accelerated it up to the speed of the wind. THat's the end of the transient condition and into the steady-state condition.
In the steady-state, the plane is drifting laterally with the wind (like a hot air balloon), while at the same time using the jet-engine thrust to overcome forward air resistance.
Hey Teacher, Teacher, please sir, can I have a gold star... pretty please
Because it depends on whether this is steady-state or a transient.
The jet engines are thrusting forward, not sideways. So there is no resisting force against the lateral wind.
If the wind has just started, Hymie is spot on - the plane will be accelerating gradually in the direction of the wind, and we don't know the forces on it, so we don't know how far it travels with the wind. It's a transient - that is to say the situation is adjusting to a new situation.
After a while, the wind has pushed on the plane (laterally) and accelerated it up to the speed of the wind. THat's the end of the transient condition and into the steady-state condition.
In the steady-state, the plane is drifting laterally with the wind (like a hot air balloon), while at the same time using the jet-engine thrust to overcome forward air resistance.
Hey Teacher, Teacher, please sir, can I have a gold star... pretty please
