How can I understand what this says? Can someone also tell me what the heck those symbols mean and where they came from?
$$\vec{p_e} = 1200 kg \cdot 5 m/s [{1 \over \sqrt{2}} , {1 \over \sqrt{2}}] \\ \vec{\Delta p} = \vec{p_e} - \vec{p_f} = 1200 [-{5 \over \sqrt{2}}, {15 \over \sqrt{2}}] kg m/s \\ |\vec{\Delta p}| = 1200 \sqrt{({5 \over \sqrt{2}})^2 + ({15 \over \sqrt{2}})^2} kg m/s = 1,3 \cdot 10^4 kgm/s$$
The arrows over the symbols mean we are dealing with vectors. These vectors are rendered in a strange format though. The first vector gives the magnitude first ($1200 kg * 5 m/s$) then the direction $[1/\sqrt{2}, 1/\sqrt{2}]$. If you multiply everything out, you can get the vector in a more traditional format: $[3000\sqrt{2}, 3000\sqrt{2}] kg\cdot m/s$.
The second vector is even more confusing in its format. The magnitude has been partially multiplied over the direction. Finishing the multiplication yields: $[-3000\sqrt{2}, 9000\sqrt{2}]kg\cdot m/s$
The third equation is simply computing the magnitude of the second vector. Using our more tradition form of the vector it would be: $$\left\vert \triangle p \right\vert = \sqrt{(-3000\sqrt{2})^2+(9000\sqrt{2})^2}kg \cdot m/s \approx 1,3 \times 10^4 kg \cdot m/s$$
The comma is simply the European form of a decimal point: $1,3 = 1.3$.
$$\vec{p_e} ... kgm/s$$in the question body? – Daniel Fischer Feb 21 '14 at 18:35