# Homework Help: Wind velocity and aircraft (answer check)

1. Jan 15, 2014

### negation

1. The problem statement, all variables and given/known data

You’re a pilot beginning a 1500-km flight. Your plane’s speed is 1000 km/h, and air traffic control says you’ll have to head 15° west of south to maintain a southward course. If the flight takes 100 min, what’s the wind velocity?

3. The attempt at a solution

veffective south = vactual + vwind

veffective south = 1500kmh^-1 / 1.667hr = ( 0, -900kmh^-1 )

vactual = (1000kmh^-1 cos 255, 1000kmh^-1 sin 255) = (-258.82kmh^-1 , -965.93kmh^-1)

vwind = veffective south - vactual

therefore

(0, -900kmh^-1 ) - (-258,82kmh^-1, -965.93kmh^-1)
= (258.82kmh^-1 , 65.93kmh^-1)
= |vwind| = SQRT [ (258.82kmh^-1)^2 + (65.93kmh^-1) ^2]

Last edited: Jan 15, 2014
2. Jan 15, 2014

### SteamKing

Staff Emeritus
I think you should punch the final numbers in your calculator, take the square root, and come up with one number for the answer.

3. Jan 15, 2014

### negation

The answer is 267kmh^-1

4. Jan 15, 2014

### haruspex

I confirm that answer.