A coniferous tree could be (from a mechanical point of view) approximated by a homogeneous right circular cone of height h = 40 m and radius r = 1.0 m. Find the maximum angle by which its axis may be displaced from the vertical axis before it starts to fall due to its weight.

A waterfall of height h = 30 m has flow rate Q = 1.2 m³·s^-1. Find the total force with which the water impacts the ground under the waterfall. Assume that the water quickly flows away from the point of impact and the depth of water under the waterfall is negligible.

Find the resistance between two neighbouring vertices of a four-dimensional cube made of wire. Each edge of the cube has a resistance R = 1 000 Ω.

Vítek would like to draw water from his well, but he does not want to haul the bucket up. Therefore, he gradually spun the water around until, at an angular velocity ω = 11 rad·s^-1, the water started to flow out of the well all by itself. Vítek knows the depth of the well (from the top edge to the bottom) is h = 47 m. The well has a circular cross-section of a radius r₀ = 1.6 m. What was the height of the water column (from the bottom of the well to the water surface) before Vítek started spinning the water around?