I was riding a bus one day and noticed that the double windows had some water be

Question

I was riding a bus one day and noticed that the double windows had some water between them. As the bus accelerated, the water collected to the sides, first forming a trapezoid and then a right triangle.

I begun wondering how it would be possible to measure the acceleration using only the geometry of the form of the amount of water.

Like, assume that at a=0 the water has height h and width w. As the bus accelerates, at some time t1 the water forms a trapezoid with the shorter side h1 ans longer side h2. The bottom has same width w.

At time t2 water has formed a triangle with height H and width w (the last moment it touches the other side of the glass). And finally at time t3 the height is y and the width is W.

In each situation, what is the acceleration of the bus?

Explanation / Answer

I think the answer can be relatively simple. The acceleration of the bus is perpendicular to the direction of gravity. Assuming that the water-air interface stays flat, you can approximate the tilt angle of the interface with respect to the horizontal, say ?, and calculate the acceleration by a=gtan?.

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