How Do You Calculate Aircraft Velocity with Wind Influence?

AI Thread Summary
To calculate the aircraft's new velocity relative to the ground, the correct approach involves using vector addition of the plane's velocity and the wind's velocity. The initial velocity of the jet is 300 mi/h due east, while the wind is blowing at 100 mi/h at 30 degrees north of east. The relative velocity equation Vpe = Vpa + Vae is appropriate, but it’s crucial to treat these as vectors rather than scalars. To find the new speed and angle, one should apply trigonometric methods, specifically the cosine and sine laws, after visualizing the vectors in a diagram. This method will yield the correct resultant velocity of the aircraft relative to the Earth.
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Relative Velocity?

OK - I'm having problems visualizing a relative velocity problem. Please let me know if I am on the right track... problem involves a jet with initial V of 300 mi/h due east that encounters winds at 100 mi/h in a direction 30 degrees north of east. I need to calculate new velocity relative to the Earth (or ground).

I believe my relative velocity equation should be Vpe (plane to earth) = Vpa (plane to air) + Vae(air to earth). I'll solve for Vpe. Does this seem right? And since I'm asked for the new velocity (vector), i believe I'd take the arccos of the Vpa/Vpe to get the angle?

Sound like a good approach?

Thanks again,
 
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What do you mean by "Vpe", etc.? They should be vectors but then "arccos of the Vpa/Vpe" doesn't make sense- you can't divide one vector by another. Draw a picture (is the wind blowing toward 30 degrees N of E or from that direction? Usually wind is given as coming from a direction but you said "in" that direction so apparently it is blowing toward that.) Once you have drawn the vectors for the jets original velocity and wind velocity, draw in the third side of the triangle- the planes new velocity. You will need to use trigonometry to solve for the new speed and angle- cosine law to find the speed and then the sine law to find the angle.
 
There was a relative velocity question where the relatives were divided and then the arccos was taken to determine the angle. It was a sample problem I viewed, hence my deduction. Had something to do with a boat crossing a river with a current and boat speed relative to shore - so I saw some simliarities with this problem...

So, it does makes sense that I would be adding the vectors for this relative velocity question? The sentence says "in a direction 30 degrees north of east" and "what is the new velocity of aircraft relative to ground"... So, I would use the sin function for the angle and how would I determine the velocity - simply the pythagorean?

Thanks again
 
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