Question

As an apple tree is transported by a truck moving left to right with constant velocity, one of its apples shakes loose and falls toward the bed of the truck. What describes the path followed by the apple, as seen by a stationary observer on the ground?

Since the apple, apple tree, and truck are all moving with constant velocity, will the apple appear to move straight down? Or, will it follow a curved path as if falling off the back of the truck? I don't know why this is confusing me, but I can't make up my mind which would be correct. There are no diagrams, or additional information given.

Answer 1

For the stationary observer on the ground, an apple falling from a moving truck will follow a parabolic path, maintaining the truck's horizontal velocity while simultaneously accelerating downward due to gravity.

Step-by-step explanation:

To determine the path of the apple as it falls from the moving truck, we need to consider the perspective of two different observers: one on the truck and one stationary on the ground. For the observer on the truck, the apple appears to fall straight down because it already has the same horizontal velocity as the truck. However, for the stationary observer on the ground, the apple will follow a parabolic path. This is because the apple retains its forward horizontal motion while also accelerating downward due to gravity. Consequently, it moves diagonally relative to the ground observer, tracing out an arc.

The concept is similar to that of the classical relativity principle, where a person on a moving ship sees binoculars fall straight down, whereas a person on the shore sees them follow a curved path. Both observers notice that the binoculars hit the base of the mast, not behind it. Likewise, the apple will land directly below its point of release as far as the truck's movement is concerned, but its path as viewed by the stationary observer will curve due to its horizontal motion at the time of release.