Find the velocity of the airplane if there was no wind

In summary, the conversation discusses finding the magnitude and direction using the cosine and sine rules. The solution shows a slight discrepancy due to rounding off and the magnitude being irrational.
  • #1
chwala
Gold Member
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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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  • #2
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.
 
  • #3
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!
 

Related to Find the velocity of the airplane if there was no wind

1. What is the formula for finding the velocity of an airplane with no wind?

The formula for finding the velocity of an airplane with no wind is v = d/t, where v is the velocity, d is the distance traveled, and t is the time taken to travel that distance.

2. How is the velocity of an airplane affected by wind?

The velocity of an airplane is affected by wind because wind can either add to or subtract from the airplane's speed. If the wind is blowing in the same direction as the airplane, it will increase the velocity. If the wind is blowing in the opposite direction, it will decrease the velocity.

3. What units are used to measure the velocity of an airplane?

The velocity of an airplane is typically measured in miles per hour (mph) or kilometers per hour (km/h).

4. Can the velocity of an airplane be negative?

Yes, the velocity of an airplane can be negative if the wind is blowing in the opposite direction and causing the airplane to slow down.

5. How can the velocity of an airplane be calculated if there is wind present?

To calculate the velocity of an airplane with wind, you will need to know the speed and direction of the wind. Then, you can use vector addition to find the resultant velocity of the airplane, taking into account the wind's effect on the airplane's speed and direction.

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