Without a diagram, I'm not entirely sure what you mean by A' and B'.

What I'm saying is, if the train is moving forward 40 mph, and you jump off of it sideways at e.g. 1 mph, then you are still moving forward 40 mph *even when you're in the air*. (Because when you're "connected" to the train, you're going forward at 40 mph. And that speed doesn't just disappear the moment you disconnect.)

So, relative to the train's new location, you'd land perpendicular. But the train has moved forward, so, relative to the ground, you don't land perpendicular from where you jumped off. (From a bird's eye view, you're moving on a diagonal. Mostly forward, but a little to the side.)

Will I be losing the train speed after the jump out from this train ?

I do not see the answer so I assume that I will be losing the train speed after the jump out from this train. Please refer (or someone else) to this (the second answer from the top)

https://www.quora.com/If-I-jump-inside-an-accelerating-train-will-I-land-at-a-spot-behind-where-I-jumped"To take a wider view the ground accelerates the entire train, including the floor you were standing on. As long as you were in contact with the floor, it can exert forces on you that accelerate you with the rest of the train. The instant you lost contact with the floor, these forces vanish (all forces are local!). In the absence of any horizontal force, your horizontal acceleration goes to zero, and the horizontal component of your velocity remains the same until you land on the floor behind where you jumped. In the train frame of reference it would seem as if there was a force pushing you backwards, but there is no such force. The train is moving faster than you in the other direction.

The idea of all forces being local seems to be contradicted by gravitational and electromagnetic forces, but no one has been able to really make sense of such forces without using the field concept. Gravitational and electromagnetic fields are considered to be at least as real by physicists today as the ordinary objects all around us, and these fields act locally to produce forces."