We are going to use the coordinate sign convention here while keeping the mirror facing the towards the negative x-axis.

The spherical mirror formula is:

$\frac{1}{u}+\frac{1}{v}=\frac{1}{f}$

differentiating both sides with respect to time, $t$,

$\frac{d}{dt}(\frac{1}{u})+\frac{d}{dt}(\frac{1}{v})=\frac{d}{dt}(\frac{1}{f})$

Since $f$ is a constant for a given mirror,

$\frac{d}{dt}(\frac{1}{f})=0$

Thus,

$\frac{d}{dt}(\frac{1}{u})+\frac{d}{dt}(\frac{1}{v})=0$

$\implies \frac{d}{dt}(\frac{1}{v})=-\frac{d}{dt}(\frac{1}{u})$

$\implies -\frac{1}{v^2}\frac{dv}{dt}=\frac{1}{u^2}\frac{du}{dt}$

Hence, the image velocity is,

$\boxed{\frac{dv}{dt}=-(\frac{v^2}{u^2})\frac{du}{dt}}$

Here, $u$ is the object distance, $v$ is the image distance, and $f$ is the focal length of the mirror.

From the given data for the concave mirror,

$u=-60\;cm$

$f=-20\;cm$ (since the focus is along the negative x-axis)

$\frac{du}{dt}=8\;cm$ (since the object is moving along the positive x-axis)

Using the mirror formula,

$\frac{1}{v}=-\frac{1}{20}+\frac{1}{60}$

$\implies \frac{1}{v}=-\frac{1}{30}$

Hence,

$v=-30\;cm$

The negative sign in $v$ indicates that the image is travelling away from the mirror in the -x direction.

Now, substituting the values of $u$, $v$, and $\frac{du}{dt}$, in the relation between image velocity and object velocity obtained above, we get,

$\frac{dv}{dt}=-\frac{900}{3600}\times 8$

$\implies \frac{dv}{dt}=-2\;\frac{cm}{s}$ **(Ans)**

If you look carefully into the animation I have attached, you will see, that at a screen that is placed equally distant to the centres of both the waves, an alternating maximum, zero, and minimum pattern is created. When we apply this concept of interference pattern to light waves, or any electromagnetic wave, we get the same result with a slight modification. With electromagnetic waves, on the screen, we get intensity patterns. Since the intensity of a wave is directly proportional to the square of the amplitude of the wave, the maxima and minima result in the same intensity. Remember that minima are the negative maxima and the square of -1 is just 1. Thus for EM waves, interference produces bright (max or min) and dark (zero displacement) patterns. We call these fringes.

**NOTE: For interference of two waves to produce fringes, they must be of the same frequency (or wavelength), else, the pattern will not be constant and won't be clearly visible.**

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It is a vector that doesn't follow vector laws.

A quantity that doesn't obey vector laws cannot be considered a vector.

Tension (or compression) in general is not a force but a pair of equal and opposite forces acting at a certain point. In problems in Physics and engineering, we often consider only one of the two forces in the tension pair and call it tension or tensile force. In this way, we can consider tension as a vector.

When you go by the layperson's definition of a tensor in Physics that says, "tensor is a physical quantity which has one magnitude and multiple directions.", you may consider tension as a tensor. However, tension does not fit the mathematical matrix in order to be a mathematical tensor. This is why the layperson's definition of a tensor isn't a valid one.

I hope my explanation helps.

]]>Here is the video of how a javelin flies.

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