How Do You Calculate the Velocity of a Ball Thrown from a Moving Train?

[leafsfan2]

Homework Statement

A man on a moving train throws a ball at a parked car. Find velocity of the ball when it hits the car if:
train is moving 21 m/s North East;
the man is walking 3.0 m/s [E35S] (relative to train)
ball is thrown 10.0 m/s [W22S] (relative to man)

Homework Equations

V_BG = V_BM + V_MT + V_TG
(B=ball, M=man, T=train, G=ground)

The Attempt at a Solution

I know how to do it if they were all either North or south, but the different directions with the angles confuses me. I've done a bunch of practice questions with only 2 other relative motions (Vxy=Vxz+Vzy), where I use trigonometry to solve for the resultant, but I don't know how to solve it with three relative motions solving for the fourth. I attempted to use trig, but got nowhere with it, and I'm assuming that's not what I should use. My guess is that I should use components? But so far all I wrote was this:
V_BG = V_BM + V_MT + V_TG

 

[SammyS]

You use trig to find the components, don't you?

I take it that E35S means 35° South of due East, etc.

Just find the x-component & y-component for each velocity vector & add them. Then find the magnitude & direction of the resultant. (Usually the positive x-axis points East, & the positive y=axis points North.)

The result looks to me like it will be pretty strange. Also the person throwing the ball must be a contortionist and left handed.

 

[leafsfan2]

Components completely slipped my mind. Thank you, it worked. I got 12m/s [E49N] so that does sound a bit odd but it's just a random question so I'm sure it doesn't matter if it's realistic

 

[SammyS]

Yes, that's a reasonable answer.

The train is moving at more than twice the speed he throws the ball, and he throws the ball in nearly the opposite direction of the train's motion.