Moving Object, Stationary Plane Mirror

Q.

A person walks with velocity $\mathrm{V}$ in a straight line forming an angle theta with the plane of a plane mirror. Find the velocity $\mathrm{V}$ relative with which he approaches his image.

Q. A man runs towards a mirror at a speed $+6\text{m/s}$. If the mirror is at rest, his image will have a velocity (with respect to man)

1. $12\text{m/s}$
2. $-6\text{m/s}$
3. $6\text{m/s}$
4. $-12\text{m/s}$

Q. The origin of $x$ and $y$ coordinates is the pole of a concave mirror of focal length $20\text{cm}$. The $\text{x-axis}$ is the optical axis with $x>0$ being the rear side of mirror. A point object at the point $(30\text{cm},1\text{cm})$ is moving with a velocity $10\text{cm/s}$ in positive $\text{x-}$direction. The velocity of the image in $\text{cm/s}$ is approximately

1. $40\hat{i}-4\hat{j}$
2. $-40\hat{i}+2\hat{j}$
3. $-40\hat{i}-2\hat{j}$
4. $-80\hat{i}+8\hat{j}$

Q. An object is approaching a fixed plane mirror with velocity $10\text{m/s}$ making an angle of ${60}^{\circ }$ with the normal to the mirror. The speed of image with respect to the mirror is

1. $15\text{m/s}$
2. $10\text{m/s}$
3. $20\text{m/s}$
4. $25\text{m/s}$

Q. A plane mirror is placed parallel to y-axis with its center at origin $(0,0,0)$. An object starts the motion in front of the mirror from position $(2,0)\text{m}$ with a velocity $(2\hat{i}+2\hat{j})\text{m/s}$. The relative velocity of image with respect to the object is along

1. positive x-axis
2. positive y-axis
3. negative y-axis
4. negative x-axis

Q. A bullet of mass $m_2$ is fired from a gun of mass $m_1$ with horizontal velocity $v$. A plane mirror is fixed to the gun facing towards the bullet. The velocity of the image of the bullet formed by the plane mirror with respect to the bullet is (Neglect the mass of mirror)

1. $(1+\frac{m_2}{m_1})v$
2. $\left(\frac{m_1+m_2}{m_1}\right)v$
3. $\frac{2(m_1+m_2)v}{m_1}$
4. $\frac{2(2m_1+m_2)v}{m_1}$

Q. An object is dropped from a height of $20\text{m}$. If a plane mirror is lying on the floor with the reflecting surface facing the object. The speed of image of the ball with respect to the ball just before striking the mirror will be
$($Take $g=10{\text{m/s}}^2)$

1. $40\text{m/s}$
2. $30\text{m/s}$
3. $10\text{m/s}$
4. $20\text{m/s}$

Q. A point object $O$ is moving with a velocity of $v$ in front of an arrangement of plane mirrors as shown in the figure. The magnitude of velocity of image in mirror $M_1$ with respect to the image in mirror $M_2$ will be

1. $3v\cos \theta$
2. $2v\cos \theta$
3. $3v\sin \theta$
4. $2v\sin \theta$

Q.

Superman is trapped in a planet full of evil superman clones, who are as strong as him! As he tries to flee the planet, unknown to him, there is a huge plane reflector suspended in the sky. As he zooms upward at 100 m/s, how fast will he see his image (which, he will mistake to be an evil clone!) zoom towards him? (The reflector is at rest, and very very far from superman at the instant.)

1. $100\frac{m}{s}$, away from him.
2. $200m/s$, towards him.
3. $100m/s$, towards him.
4. $200\frac{m}{s}$, away from him.

Q. An object is performing uniform circular motion in a horizontal $xy$ - plane in front of a plane mirror kept perpendicular to $xy$ - plane and reflecting surface facing the object. If the object is revolving in an anti-clockwise direction with speed $v$, then identify the correct statement regarding the motion of the image with respect to ground.

1. The image is moving on a straight line with speed $\frac{v}{\sqrt{2}}$
2. The image is revolving in clockwise direction with speed $2v$ on circular path
3. The image is revolving in anti-clockwise direction with speed $2v$ on circular path
4. The image is revolving in clockwise direction with speed $v$ on circular path

Q. A person $AB$ of height $170\text{cm}$ is standing in front of a plane mirror. His eyes are at height $164\text{cm}$. At what distance from $P$ should a hole be made in the mirror so that he cannot see his hairs?

1. $167\text{cm}$
2. $161\text{cm}$
3. $163\text{cm}$
4. $165\text{cm}$

Q. The origin of $x$ and $y$ coordinates is the pole of a concave mirror of focal length $20\text{cm}$. The $\text{x-axis}$ is the optical axis with $x>0$ being the rear side of mirror. A point object at the point $(30\text{cm},1\text{cm})$ is moving with a velocity $10\text{cm/s}$ in positive $\text{x-}$direction. The velocity of the image in $\text{cm/s}$ is approximately

1. $-40\hat{i}+2\hat{j}$
2. $-40\hat{i}-2\hat{j}$
3. $-80\hat{i}+8\hat{j}$
4. $40\hat{i}-4\hat{j}$

Q. A ball is projected from top of a table with initial velocity $u$ at an angle $\theta$ with the horizontal as shown in the figure. The motion of image of ball with respect to the ball will be
$($Consider the plane mirror of sufficient height$)$

1. a projectile
2. straight line along vertical direction
3. straight line along horizontal direction
4. straight line or projectile depends on angle $\theta$

Q. A plane mirror is placed along the vertical plane (yz-plane). If a particle is also projected in the vertical plane with speed of projection $10\text{m/s}$ and angle of projection as ${60}^{\circ }$ from the normal direction to mirror. The point of projection is at a distance of $5\text{m}$ from the mirror, and the particle is directed towards the mirror. The magnitude of velocity of approach of particle and image, just before the particle touches the mirror is

1. $10\text{m/s}$
2. $10\sqrt{3}\text{m/s}$
3. $5\text{m/s}$
4. $5\sqrt{3}\text{m/s}$