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2

But my problem is that I don't understand how a force can be a vector, in my head I see it as a direction vector and some power number Right. If the direction is a "unit" vector, then you can compare the magnitudes of different forces to compare the strengths. But you can multiply the magnitude and the direction to get a new vector that contains ...

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Force has both a magnitude and direction, which are the properties of a vector. The magnitude can be given by $\vec{F} = G\frac{M_1M_2}{\vec{r^2}}$ where $G$ is the gravitational constant and $M_1,M_2$ are the masses. the distance from each other is represented by the vector $\vec{r}$ which will be the displacement from the origin.

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Hint: Use the final equation from my other answer here: $$E(0,t) = E_0\exp(-i\bar{\omega}t)\frac{\sin[(N/2)\Delta\omega t]}{\sin[(1/2)\Delta\omega t]}.$$ This is already a function of time. Now, $I(0,t)\propto |E(0,t)|^{2}$, so just square that function for the intensity (normalize to remove constants if you like). That will ...

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This is a standard projectile motion problem with the complication that the projectile collides elastically with vertical walls. Assuming that the only force exerted on the projectile by the walls is in a direction which is normal to the walls then: the vertical velocity does not change, and the horizontal velocity reverses direction but the magnitude ...

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Of course, you can do it with Matlab, Mupad, Maple, Mathematica or even the Smart Math Calculator. Use this method: First define your variables with your units of choice, then tell the programm what the conversion factors from the given units to the target units are, for example, if you have km/h and need m/sec define 1km as 1000m and 1sec as h as 60² ...

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