Find the velocity of the airplane if there was no wind

[chwala]

Homework Statement

See attached

Relevant Equations

Understanding of vectors

Find the question and its solution below;

Ok i realized that we could also use cosine rule here, in my approach i considered the sketch below;

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

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.

 

[mjc123]

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.

 

[chwala]

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!