In a small coastal village, there lived two friends, Eshaan and Aolani. One sunny morning, they decided to go to the nearby beach to relax and enjoy the water. Eshaan, who was of average height, ventured first into the calming waves of the ocean. He walked straight into the water until it reached right below his knees. Meanwhile, Aolani, who was slightly taller than Eshaan, walked to a different spot along the shore where she found a shallow trench running parallel to the water's edge. She stepped into this depression and the water level came up exactly to her knees.

Both of them stood in the water watching the distant boats and enjoying the gentle touch of the waves. Unexpectedly, a small wave approached from the open sea. As the children continued to play in the water, a curious question arose. If Eshaan and Aolani remained stationary, what would each observe as the wave reached them? Specifically, would they both see the wave reaching the same height on their bodies and what difference, if any, would the trench that Aolani stood in make to her observation?

Provide a brief response.
Eshaan, standing in the flat part of the beach with water just below his knees, would observe the incoming wave as it actually was - a slight rise in the height of the water. As a small wave typically would not change the overall water level significantly, Eshaan would likely see the water level rise up a bit on his legs, possibly to his knees, depending on the height and strength of the wave. However, considering that the wave is described as small, it might not make a noticeable difference in Eshaan's perception of water height relative to his body.

In contrast, Aolani stood in a trench. This existing depression would have an impact on the way she observed the wave. As the wave entered the trench, the wave's height would be augmented by the depth of the trench, making the wave appear taller relative to her surroundings and to Aolani herself. Since water seeks to level itself, the wave height would need to overcome the depth of the trench before it could rise relative to the original water level. Therefore, if the wave was sufficiently strong or high to fill the trench and continue rising, Aolani would see the wave reaching higher on her body than Eshaan experienced, possibly surpassing her knees, even though they are taller. If the wave was not strong enough to fill the trench and rise above it, the wave might not seem to alter the water level around her significantly.

The critical point here is that the appearance of the water level change depends on their respective environments. Eshaan, being on a flat surface, would see the wave's effect in a straightforward manner, whereas Aolani would experience an amplified effect due to the initial depression she stood in. The trench can either exaggerate the perceived height of a wave if the wave is strong enough or obscure a smaller wave's effect by absorbing its energy and not allowing the water level to rise visibly at all. Hence, their observations would differ based on both their differing heights and the presence of the trench.