Final answer:
A ball dropped from a bus moving at constant velocity appears to fall vertically for a passenger on the bus due to shared horizontal momentum, while an outside observer sees a parabolic trajectory, illustrating the relativity of motion between different frames of reference.
Step-by-step explanation:
If you are standing in a bus that moves at constant velocity and drop a ball from your outstretched hand, you will see its path as a vertical straight line because you are moving with the same horizontal velocity as the ball. However, a friend standing at the side of the road will see a different path. To your friend, the ball will appear to follow a parabolic trajectory, because the ball retains the horizontal velocity of the bus as it falls. This effect is due to relativity of motion.
In your frame of reference inside the bus, you and the ball are both moving at the same horizontal velocity, and thus the ball appears to only be influenced by gravity when you drop it. This is why it falls straight down relative to your position. However, in your friend's frame of reference at the side of the road, the ball is moving forward (at the same speed as the bus) while also being pulled down by gravity, resulting in a parabolic path.
This concept can be further illustrated by frame of reference examples such as someone driving a car toward the east and an observer standing still. The perceived direction and motion of objects can vary significantly based on the observer's frame of reference.