Relative velocity of a plane question

[mousemouse123]

an aircraft must fly at a velocity of 150m/s[n35e] if there were no wind to reach its destination. a wind from the west of 25m/s is present for the whole flight. calculate the velocity the pilot must maintain to reach her destination in time. i started by finding the velocity of the plane in the east west dimenson. and got 122m/s [e] would i just add this number to 25 to get the right answer?

 

[tiny-tim]

hi mousemouse123!

you need to draw a vector triangle …

what does it look like? ​

 

[mousemouse123]

hi mousemouse123!

you need to draw a vector triangle …

what does it look like? ​

gee thanks... i drew a vector triangle already... that's how i got the velocity in the east west direction...:grumpy:

 

[madmac95]

I found that the velocity of the plane to the ground was 165.6m/s (N42E).
I did this using the vector diagram then the cosine law to find the velocity of the plane to the ground, then the sine law to find the angle it travels.

 

[Nickie]

No, simply adding the velocity in the east-west dimension to the wind speed will not give the correct answer. This is because the wind affects the velocity of the plane in both the east-west and north-south dimensions. To calculate the correct velocity the pilot must maintain, you will need to use vector addition to find the resultant velocity. This can be done by breaking down the velocities into their respective components and then adding them together. Once you have the resultant velocity, you can compare it to the required velocity of 150m/s to determine if the pilot needs to adjust their speed or direction to reach their destination in time.