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

A h = 30 m high waterfall has flow rate Q = 1,2 m³·s^-1. Find the total force with which 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 get some water from his well, but he does not want to keep pulling the bucket up. Therefore, he gradually stirred the water around faster and faster until, at an angular velocity ω = 11 rad·s^-1, the water started flowing out of the well all by itself. Vítek knows the depth of the well (from the top edge to the ground at the bottom) h = 47 m. The well has a circular cross-section with 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?