Physics - Geometrical Optics Question with Solution | TestHub

For a convex mirror, the focal length is $f=\frac{R}{2}=\frac{20}{2}=+10\text{ m}$.

Using the mirror formula, $\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$

For the first position of the image, $v_1=\frac{25}{3}\text{ m}$:

$\frac{1}{u_1}=\frac{1}{10}-\frac{3}{25}=\frac{5-6}{50}=-\frac{1}{50}$

$u_1=-50\text{ m}$

For the second position of the image, $v_2=\frac{50}{7}\text{ m}$:

$\frac{1}{u_2}=\frac{1}{10}-\frac{7}{50}=\frac{5-7}{50}=-\frac{2}{50}=-\frac{1}{25}$

$u_2=-25\text{ m}$

The distance moved by the object is $\Delta u=|-25-(-50)|=25\text{ m}$.

The speed of the object is $v_{obj}=\frac{\Delta u}{\Delta t}=\frac{25}{30}=\frac{5}{6}\text{ m/s}$.

Converting the speed to km/hr:

$v_{obj}=\frac{5}{6}\times \frac{18}{5}=3\text{ km/hr}$

Answer: 3