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(D) The mirror used in a car as a rear-view mirror is a convex mirror.For a spherical mirror,the velocity of the image $V_I$ with respect to the mirro

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$0.1$

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(D) The mirror used in a car as a rear-view mirror is a convex mirror.For a spherical mirror,the velocity of the image $V_I$ with respect to the mirror is given by $V_{I/m} = -m^2 V_{O/m}$,where $m$ is the magnification and $V_{O/m}$ is the velocity of the object with respect to the mirror.Given:Relative speed of car $B$ with respect to car $A$ is $V_{O/m} = 40 \, ms^{-1}$.Focal length of the convex mirror $f = +10 \, cm = +0.1 \, m$.Object distance $u = -1.9 \, m$.The magnification $m$ is given by $m = \frac{f}{f - u}$.Substituting the values: $m = \frac{0.1}{0.1 - (-1.9)} = \frac{0.1}{2.0} = \frac{1}{20}$.Now,calculate the velocity of the image:$V_{I/m} = -m^2 V_{O/m} = -(\frac{1}{20})^2 	imes 40 = -\frac{1}{400} 	imes 40 = -0.1 \, ms^{-1}$.The negative sign indicates that the image moves in the direction opposite to the object's motion relative to the mirror. The speed of the image is $0.1 \, ms^{-1}$.

$(i)$ Velocity of image	$(a) \; 2 \; m/s$
$(ii)$ Velocity of image with respect to mirror	$(b) \; 20 \; m/s$
$(iii)$ Velocity of image with respect to object	$(c) \; 11 \; m/s$
$(iv)$ Velocity of image if mirror is stopped	$(d) \; 22 \; m/s$

Car $B$ overtakes another car $A$ at a relative speed of $40 \, ms^{-1}$. How fast will the image of car $B$ appear to move in the mirror of focal length $10 \, cm$ fitted in car $A$,when the car $B$ is $1.9 \, m$ away from the car $A$? (In $ms^{-1}$)

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