Question

Determine the velocity of image with respect to mirror:

• A.
  $(0.25\hat{i}-0.5\hat{j})\text{m/s}$
• B.
  $(0\hat{i}-0.5\hat{j})\text{m/s}$
• C.
  $(0.5\hat{i}-1\hat{j})\text{m/s}$
• D.
  $(0.1\hat{i}-0.5\hat{j})\text{m/s}$

Answer 1

The correct option is B

$(0\hat{i}-0.5\hat{j})\text{m/s}$

Velocity of image along $\text{x-axis}$	velocity of image along $\text{y-}$axis
velocity of object wrt mirror ${\overrightarrow{v}}_{o/m}{]}_x={\overrightarrow{v}}_o{]}_x-{\overrightarrow{v}}_m{]}_x$ ${\overrightarrow{v}}_o{]}_x=4\sqrt{2}\cos {45}^{\circ }=4\text{m/s}$ ${\overrightarrow{v}}_m{]}_x=5\cos {37}^{\circ }=4\text{m/s}$ $\therefore {\overrightarrow{v}}_{o/m}{]}_x=({\overrightarrow{v}}_o{]}_x-\overrightarrow{v}{]}_m)$ $=4-4=0\text{m/s}$	$\overrightarrow{v_o}{]}_y=4\sqrt{2}\sin {45}^{\circ }=4\text{m/s}$ $\overrightarrow{v_m}{]}_y=5\sin {37}^{\circ }=3\text{m/s}$ velocity of object wrt mirror ${\overrightarrow{v}}_{o/m}{]}_y={\overrightarrow{v}}_o{]}_y-\overrightarrow{v}{]}_y$ $=4-3=1\text{m/s}$
Velocity of image wrt mirror ${\overrightarrow{v}}_{i/m}{]}_x=-m^2{\overrightarrow{v}}_{o/m}{]}_x$ $m=\frac{f}{f-u}=\frac{-10}{-10-(-30)}=\frac{-1}{2}$ ${\overrightarrow{v}}_{i/m}{]}_x=-\left(\frac{-1}{2}\right)\times \left(0\right)$ $\therefore {\overrightarrow{v}}_{i/m}=0\hat{i}\text{m/s}$	Velocity of image wrt mirror ${\overrightarrow{v}}_{i/m}{]}_y=m{\overrightarrow{v}}_{o/m}{]}_y$ $\because m=\left(\frac{-1}{2}\right)$ ${\overrightarrow{v}}_{i/m}{]}_y=\left(\frac{-1}{2}\right)\times \left(1\right)=-0.5\text{m/s}$ $\therefore {\overrightarrow{v}}_{i/m}=0\hat{i}-0.5\hat{j}\text{m/s}$