I am sitting on a train car traveling horizontally at a constant speed of 50 m/s. I throw a ball straight up into the air.

Describe the motion of the ball as I see it. Is the path taken by the ball different than if I was sitting at rest at home and I threw a ball straight up into the air?

I am sitting on a train car traveling horizontally at a constant speed of 50 m/s. I throw a ball straight up into the air. Before, the ball gets separated from my hand, both me the ball will be moving with velocity of 50 m / s in horizontal direction.

As soon as ball is separated from the hand, it acquires addition velocity in upward direction and acceleration in downward direction. This will give relative velocity to the ball with respect to me. So I will see the ball going in upward direction under gravitational acceleration. It appears as if I am sitting at rest and ball is going in upward direction under deceleration. My motion at 50 m/s will have no effect on the motion of ball in upward direction, according to first law of Newton. It is so because ball too will be moving in forward direction with the same speed which will not be visible to me because I too am moving with the same speed.

If I am sitting at rest at home and I threw a ball straight up into the air, I will have the same experience of seeing ball going in similar way as described above.