[s1artibartfast]

>But the water droplets/sand particles do NOT form a straight line if you accelerate the jug. You have to decelerate the jug with exactly the right timing to form a straight line, not accelerate it.

You can make a right triangle via either acceleration or deceleration at the same rate as gravity. However, you can only make an Isosceles Right Triangle with acceleration

Vertical position is a function of t^2. If you have constant horizontal velocity, you get a concave curve like this: https://www.wolframalpha.com/input?i=Y%3D-1x%5E2

Accelerating the horizontal velocity leads to a triangle like this: https://www.wolframalpha.com/input?i=Y%3D-x

[SamBam]

Actually a constant horizontal velocity will make a straight vertical line of droplets under the jug. This is because the drops will have the same horizontal velocity as the jug.

You can see that here: https://demonstrations.wolfram.com/TrajectoryOfABomb/

At any time, the first bomb is always directly under the plane. This means all subsequent bombs will also be under the plane.

[s1artibartfast]

That's true. In the zero acceleration case you get a vertical straight line. If you have acceleration or deceleration equal to G, you get a straight angled line. If you have any acceleration or deceleration that doesn't match G, you get a curve