To determine the highest place from which a coin can be dropped without landing on its edge, we need to consider the stability of the coin during its fall and its physical properties.
The stability of a falling object depends on its rotational stability. A coin typically has a circular shape and tends to rotate as it falls due to air resistance. The coin's stability depends on its moment of inertia, which is a measure of how the mass is distributed around its axis of rotation.
The critical condition for a coin to land on its edge is when its moment of inertia around the edge is equal to or less than its moment of inertia around the face. This can happen if the coin is dropped from a height that allows it to complete a full rotation before reaching the ground.
However, the specific dimensions and mass distribution of a coin can vary. Therefore, the highest place from which a coin can be dropped without landing on its edge would depend on the specific coin's size, shape, and mass distribution.
In practice, it is challenging to determine the exact height from which a coin will consistently land on its edge. It is more likely that the coin's landing orientation will be random due to factors such as air currents and slight variations in the coin's shape.