while sitting in a moving bus you throw an apple up into the air the apple will land back in your hand?

Answer 1

Yes, the apple will land back in your hand—if the bus is moving at a constant velocity in a straight line. In this case, the apple shares the same horizontal velocity as the bus when you throw it, so it continues to move forward with the bus while in the air. From your perspective, it appears to go straight up and down.

However, if the bus is accelerating, decelerating, or turning, the apple will not land back in your hand:

1. If the bus accelerates, the apple will lag behind your hand.
2. If the bus decelerates, the apple will move forward relative to your hand.
3. If the bus turns, the apple will continue moving in a straight line (due to inertia) and miss your hand.

This highlights an important lesson: even experts can sometimes overlook assumptions, like uniform motion in this case. To fully answer questions like this, it's crucial to consider all possible scenarios and make implicit assumptions explicit.

Answer 2

Yes it will! Even though the bus is moving and you are sitting on the bus, it means you are moving at the same velocity with the bus so that a stationary observer will see you, the bus and the apple all moving at the same velocity! However the relative velocity between you and the bus along the horizontal axis is ZERO, it follow that of the apple is zero as well.