Direction of Light - Laser Beam Moving Sideways at Relative Speed

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If you send a laser beam in a car at a plate while moving it sideways at a relative speed, how will the beam act?

a) Will it follow the forward direction of the emitter and hit the plate? (The rest frame will see it move directily forward and see it not hitting the plate)

b) If the rest-frame saw this, would he see the beam move in a sloped angle compared to himself, (a straight angle towards the plate in the car)

I am just reading the introduction to relativity... You all know the illustration of the train and the beam that moves "sideways" to show how a clock is slowed down. But it just makes me wonder that light will follow the emitters sideway velocity. Shouldn't it be "detatched" from the moving frame and move directly forward. Or does it move at an angle so in both cases it hits the direct point of aiming for the laser.