Wind velocity and aircraft (answer check)

[negation]

Homework Statement

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?

The Attempt at a Solution

v_{effective south} = v_actual + v_wind

v_{effective south} = 1500kmh^-1 / 1.667hr = ( 0, -900kmh^-1 )

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

v_wind = v_{effective south} - v_actual

therefore

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

 

[SteamKing]

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

 

[negation]

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

The answer is 267kmh^-1

 

[haruspex]

I confirm that answer.