Respuesta :
Answer:
Magnitude of the velocity of image is 2 m/s
Explanation:
As we know that the mirror's formula for convex lens,
[tex]\frac{1}{v}+\frac{1}{u}= \frac{1}{f}[/tex]
Given that the ant is 15 cm from the convex mirror,
[tex]u=15 cm[/tex]
And focal length of the mirror is,
[tex]f=10 cm[/tex]
And the ant is moving towards the mirror,
[tex]\frac{du}{dt}=0.5m/s[/tex]
Now calculate v,
[tex]\frac{1}{v}= \frac{1}{10}-\frac{1}{15} \\\frac{1}{v}=\frac{3-2}{30} \\v=30 cm[/tex]
Now differentiate the mirror's formula with respect to t and in this focal length is constant.
[tex]-\frac{1}{v^{2} }\frac{dv}{dt}-\frac{1}{u^{2} }\frac{du}{dt} =0\\ \frac{dv}{dt}=-\frac{v^{2} }{u^{2} } \frac{du}{dt}[/tex]
Now put all the variables to get velocity of image,
[tex]\frac{dv}{dt}=-(\frac{30}{15})^{2} (0.5)\\\frac{dv}{dt}=4\times 0.5\\\frac{dv}{dt}=-2 m/s[/tex]
Therefore, the velocity of image is -2 m/s negative sign means that the direction of velocity of image is opposite to direction of velocity of ant.
