I have a problem concerning the motion in different frames of reference. This example confused me:
We've got a train which is moving and we declare the rail was our inertial frame of reference (with velocity $v=0$).
- In the first case, the velocity of the train is constant. If we're on the train resting in one place and we throw a ball in the air straight up, it lands again in our hand (so we're in the inertial frame of reference of the with constant speed moving train). This is because as we throw the ball in the air we don't only give the ball a tangential speed (regarding the floor of the train), but also a parallel speed (which equals the speed of the train). That's why it lands in our hand again. Our friend how's outside sees as we throw the ball, but to them, the ball seems to move parabolically (they're in the inertial frame of reference of the rail). This is because the train moves with a velocity parallel to the rails and with the train the ball does. This velocity is going to be added to the velocity the ball has as it's thrown in the air.
This makes all sense to me, but the next example confused me:
- Now our train has an acceleration. As we are in a state of rest on the train and throw the ball up, it accelerates (if a is the acceleration of the train and g is the gravitational acceleration, then the acceleration of the ball is the vectorial sum of the two accelerations). But to our friend, it moves linear (up and down). In the book that I read (Paul A.Tippler and Gene Mosca: Physik, 7.Auflage, Seite 154) it stated that this is because the motion of free fall is independent of the motion of the train.
But didn't we state in the first example the opposite? Didn't the ball land in our hand because the motion of the train gave the ball a velocity parallel to the ground of the train? Why is that not the case in the accelerated frame of reference?