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A plane mirror moves towards the object with a velocity of 2m/s and the object itself moves towards the mirror with a velocity of 5m/s. What is the velocity of the image approaching towards the object?​

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okpalawalter8

We have that  the velocity of the image approaching towards the object is

[tex]x=3.33m/s[/tex]

From the question we are told

A plane mirror moves towards the object with a velocity of 2m/s and the object itself moves towards the mirror with a velocity of 5m/s. What is the velocity of the image approaching towards the object?

Generally the equation for the velocity of the image  is mathematically given as

[tex]\frac{1}{f}=\frac{1}{v}+\frac{1}{u}\\\\Therefore\\\\\frac{1}{2}=\frac{1}{x}+\frac{1}{5}\\\\\frac{1}{x}=\frac{1}{2}-+\frac{1}{5}\\\\\frac{1}{x}=0.3[/tex]

[tex]x=3.33m/s[/tex]

Therefore

the velocity of the image approaching towards the object is

[tex]x=3.33m/s[/tex]

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https://brainly.com/question/12595620?referrer=searchResults

The  constructor equation of the geometric optics allows to find the result for the speed of the image is  7 m/s

Geometric optics analyzes the formation of images with different objects, for this it uses the  constructor equation

          [tex]\frac{1}{f} = \frac{1}{p} + \frac{1}{q}[/tex]

Where f is the focal length, p the distance a to the object and q the distance to the image

In this case we have a plane mirror, a plane object has its radius of curvature at infinity (f = ∞), consequently

          p = q

If we derive this expression with respect to time

         [tex]\frac{dp}{dt} = \frac{dq}{dt}[/tex]

The speed of the object and the image is the same.

In all these equation is the mirror or lens are considered fixed in space

In this case we have that the object moves towards the mirror at v₀ = 2 m / s and the mirror moves towards the object at [tex]v_m[/tex] = 5 m / s

To consider the mirror fixed in space, we must find the relative velocity of the object with respect to the mirror; the body approaches the speeds add                

             [tex]v_{om} = v_o +v_m[/tex]

Where [tex]v_{om}[/tex] speed of the object with respect to the mirror, v₀ and [tex]v_m[/tex] are the velocities of the object and the mirror, respectively

         [tex]v_{om}[/tex] = 5 + 2

         v_{om} = 7 m / s

The speed of the image and the object are equal, therefore the image speed is:

            v = 7 m / s

In conclusion using the  constructor equation allow to find the result for the image speed is 7 m / s

           

Learn more here: brainly.com/question/3795433

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