Find the velocity of the airplane if there was no wind

AI Thread Summary
The discussion focuses on calculating the velocity of an airplane without wind using the cosine and sine rules. The calculated magnitude of velocity is 164.2, with a direction angle of approximately 32.56 degrees. Participants note small discrepancies in their results, attributing these to rounding errors. The conversation emphasizes the challenges of achieving precise values in calculations involving irrational numbers. Overall, the calculations and methods discussed are deemed correct despite minor variations.
chwala
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Homework Statement
See attached
Relevant Equations
Understanding of vectors
Find the question and its solution below;
1640087655606.png
Ok i realized that we could also use cosine rule here, in my approach i considered the sketch below;

1640087758359.png


##V_b= 18,125- (2×50×125×cos 135)##
##V_b=164.2##

To find direction, i used sine rule;
##\frac {125}{sin α}##=##\frac {164.2}{sin 135}##
##α=32.56##

Would this be correct? ...i can see there is a small difference on the value of the magnitude.
 
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I got similar small discrepancies. It's probably due to rounding off. 6.5 units is 162.5 mph, and the magnitude is certainly not exactly 6.5 units - it's irrational.
 
mjc123 said:
I got similar small discrepancies. It's probably due to rounding off. 6.5 units is 162.5 mph, and the magnitude is certainly not exactly 6.5 units - it's irrational.
Cheers mjc123. Bingo!
 
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