# Galilean Transformation

## Homework Statement

a railcart A moves in a fixed accelaration $$a_1=a_1 \hat{x}$$ ($$a_1$$ is relavive to earth) at moment t=0 a ball is thrown from it in the velocity $$v_0$$ ($$v_0$$ is relative to the railcart A) and with the angle $$\alpha$$ above the horizon. the velocity of the railcart when the ball was thrown was $$\vec{v_1}=v_1\hat{x}$$ ($$v_1$$ is relavive to earth). (the mass of the ball is neglectable relavtively to the railcart so that the act of throwing the ball doesnt affect the railcart)
behind railcart A moves another railcart B and on it a man. railcart B moves in a fixed accelaration $$a_2=a_2 \hat{x}$$ ($$a_2$$ is relavive to earth) the velocity of the railcart B when the ball was thrown was $$\vec{v_2}=v_2\hat{x}$$($$v_2$$ is relavive to earth)
the man on railcart B sees the ball moving in a straight line. what should be $$\alpha$$ for it to happen? (you can state $$\alpha$$ as its tan($$\alpha$$)

## The Attempt at a Solution

for the man this is true
$$\frac{v_y}{v_x}=\frac{F_y}{F_x}$$
i tried to use the galilean transformation
but i dont seem to pull it off

this question is really hard in my opinion
if you can give me a hand here