Question : A ship is sailing 45m/s due south-east, while the wind speed is 20m/s from west.Find the magnitude and the direction of the wind velocity relative to the ship

Answer given is 33.94 m/s ; Angle is 339.6.

I'm stuck at the middle.someone help out this.
This what I do :

let s=ship
w=wind
V=velocity
So, resolve in terms of vector

Vs = 45cos45 I - 45sin45 j

Vws = 20 I

Vws = Vw - Vs
Vw = 20 I + 45cos45 I -45sin45 j
= 51.82 I - 31.82 j

Magnitude = sguare root of (51.82^2 + 31.82^2 )
= 60.81 m/s
this what answer I get and its wrong.the correct answer is 33.94 m/s and angle of 339.6.Can someone really guide me the steps and working ? Thanks you very much for your concern.

You were fine up to here:

Vws = Vw - Vs

It appears that you are using the term Vw as the relative velocity and Vws as the true wind speed. The equation to use for the velocity of the wind relative to the ship is the difference between the velocity of the wind and the velocity of the ship. If we use the term Vr to mean the relative velocity of the wind to the ship, you have:

Vr = Vw - Vs
So:
Vr = (20 I) - (45cos45 I - 45cos 45 j)
Can you take it from here?

Oh yeah I mistakely wrote it.thanks for the teaching by the way