Recent content by PeroK

Note that any point on the unit circle has coordinates ##(\cos \theta, \sin \theta)##. This is perhaps the simplest way to define sine and cosine in the first place. The negative y-axis is at an angle of ##3\pi/2##. And the angle ##3\pi/2 - x## is an angle ##x## clockwise from the negative...

Here's another way to look at it. There are no external forces on the large mass M. A small mass, m, is fired at a known speed (the external force on m is already accounted for in its specified momentum). The mass m collides inelastically with the mass M. There are no external forces in the...

... I don't see why analysing forces was necessary, if you are given everything you could possibly know about momentum!

Okay, but that was my first step. That leads directly to a differential equation: $$\frac{d v}{dt} = \frac 1 {M(t)}k(u-v)$$where ##k = \frac{dm}{dt}## is the constant rate of mass being expelled.

Here's my starting point. In the rest frame of the container, a small mass of water ##\Delta m## is ejected in time ##\Delta t## at speed ##u -v##. Conservation of momentum gives: $$\Delta m(u-v) = (M(t) + \Delta m)\Delta v \approx M(t)\Delta v$$

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That's what I get with the assumption that the jet is never a significant distance from the container.

The simplest interpretation is that the cannon follows the container and effectively all the water ejected is in the container at time ##t##. In that case, the cannon does not recoil. Does that give the expected answer?

If this is not political, then neither is the alternative view. Poor or corrupt government is a factor, but underdeveloped countries have been kept underdeveloped by US policy (and, to some extent the policy of Western nations). The priority is the profits of US corporations. These are...

Did you take into account that the water takes an increasing finite time to reach the container?

Two points of view are: Quantum Fields are reality; and, reality can only be described mathematically - fundamentally through quantum fields. I lean towards the latter. That there is a physical universe out there, and our best way to describe it is through QFT. This also allows us to have...

Belle and Sebastian; The Flashing Blade (I still remember the theme song!).

List them and see what happens when you make two balls the same.

The idea of fixing the yellow ball is that it picks out the set of solutions that cannot be equivalent under rotation. If there were, say, two balls of each red blue and yellow, then you could fix the two yellows in positions 1,2 then 1 3 then 1, 4. Those solutions cannot be equivalent under...

The discharge breaks the symmetry.