What is the velocity (in cm/s) of image in situation shown below ($O$ object, $\mathrm{f}=$ focal le

Question

What is the velocity (in cm/s) of image in situation shown below ($O$ object, $\mathrm{f}=$ focal length). Object moves with velocity $10 \mathrm{~cm} / \mathrm{s}$ and mirror moves with velocity $2 \mathrm{~cm} / \mathrm{s}$ as shown

Professor PC Thomas Classes · Answer

$\begin{aligned} \frac{1}{y}+\frac{1}{-x_1} & =\frac{1}{10} \ \frac{1}{y} & -\frac{1}{10}=\frac{1}{10} \Rightarrow y=5 \mathrm{~cm}\end{aligned}$ \ $\begin{aligned} & \frac{d x}{d y}=10 \mathrm{~cm} / \mathrm{s}, \frac{d\left(x+x_1ight)}{d t}=2 \mathrm{~cm} / \mathrm{s} \ & \frac{d y}{d t}=v_1=2 \ & \frac{d y}{d t}=\left(\frac{y^2}{x_2}ight) \frac{d x_1}{d t} \Rightarrow v_1-2=\left(\frac{5}{10}ight)^2(-8) \Rightarrow v_1=0\end{aligned}$