How would a dropped ball behave on a moving bus?

Question

A young girl standing in the aisle of a parked bus tosses a ball straight up in the air and lets it drop at her feet. The same result occurs when the bus is moving in a straight line at constant speed.

Would the result be the same if the bus were accelerating when the ball was tossed? If the girl started running down the aisle of the bus after tossing the ball? If the bus made a turn to the left while the ball was tossed? Why or why not?

Answer 1

If the bus is moving at a constant speed, theoretically, the ball will bounce straight up and down.  Since its impossible to have a perfectly level road and maintain and EXACT speed.  The ball will definitely move opposite in direction to where the acceleration occurs.

If the bus is turning while the ball is dropped it will fall to the outside of the turn in a straight line (again theoretically) since this is not a lineal acceleration.  

Answer 2

Relativity!

Ok the ball has momentum, so when the girl is stationary and she drops it, it gains momentum and drops towards the Earth straight down.

When on the bus she and the ball are moving at the same velocity as the bus the, ball has momentum in the direction of the moving bus. She drops it and it drops straight down TO HER.

To someone observing from outside the bus the ball drops in a curve as the ball still has the momentum from the buses movement.

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If the bus is accelerating then the ball will follow a curve as the ball retains the same momentum, but the girl and the bus are gaining momentum again causing the ball to make a curve when dropped.

If she runs to catch the ball after throwing (I.e. accelerating herself in the opposite direction of the bus) she is retaining the same momentum (vector) as the ball and hence will be directly below it to catch it.

If the bus makes a turn it is just like the bus accelerating but now in the left direction, thus the ball will appear to move in the right direction relative to the girl, but relative to the ball the bus has moved in a left direction.

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Effectively the ball is staying still in all these scenarios and it is the world moving around it...If that doesn't confuse you...