This simulation shows a bucket full of water. The bucket has a hole in its right side - you can use the slider to change the location of the hole. Where do you think the hole should be placed so that the water shoots out farthest horizontally from the base of the bucket?

This problem actually combines fluids with ideas from projectile motion. You can use Bernoulli's equation to determine how fast the fluid emerges from the hole - we assume the fluid has no viscosity and that the velocity of the fluid is entirely horizontal when it emerges from the hole. Then, you can determine how long it takes to fall to the level of the bottom of the bucket, and how far it travels horizontally in that time. So, it's a nice combination of concepts.

Notice how the maximum horizontal distance compares to the height of the bucket, and also see if you can spot a symmetry here in how far horizontally the water travels as a function of the position of the hole.

Simulation written by Andrew Duffy, and first posted on 7-25-2018.