A billiard table whose length and width are as shown in the figur… - Vidyadip

MCQ

A billiard table whose length and width are as shown in the figure. $A$ ball is placed at point $A$. At what angle ‘$\theta $ ’the ball be projected so that after colliding with two walls, the ball will fall in the pocket $B$ .Assume that all collisions are perfectly elastic (neglect friction)

✓
$\theta = cot^{-1}\, \frac{{2a - c}}{{2b}}$
B
$\theta = cot^{-1}$$\frac{{2a - c}}{{2b}}$
C
$\theta = tan^{-1}$$\frac{{c - a}}{{2b}}$
D
$\theta = cot^{-1}$$\frac{{c - a}}{b}$

✓

Answer

Correct option: A.

$\theta = cot^{-1}\, \frac{{2a - c}}{{2b}}$

a
$y=a-b$

$=a-(b-(a-c) \tan \theta) \cot \theta$

$=a-b \cot \theta+a-c$

$\tan \theta=\frac{b}{y}$

$\tan \theta=\frac{b}{2 a-c-b \cot \theta}$

$(2 a-c) \tan \theta-b=b$

$\tan \theta=\frac{2 b}{2 a-c}$

$\cot \theta=\frac{2 a-c}{2 b}$

$\theta=\cot ^{-1} \frac{2 a-c}{2 b}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from 5.work,energy,power and collision→5.work,energy,power and collision — all question types→Physics STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

A simple pendulum with length $L$ and mass $m$ of the bob is vibrating with an amplitude $A$. The maximum tension in the string is

A block of ice at $-20\,^oC$ having a mass of $2\, kg$ is added to a $3\, kg$ water at $15\,^oC$. Neglecting heat losses and the heat capacity of the container

The pressure of a molecular gas at constant volume depends on:

When the displacement of a simple harmonic oscillator is one third of its amplitude, the ratio of total energy to the kinetic energy is $\frac{x}{8}$, where $x=$_____________.

A body falling freely under gravity passes two points $30\,m$ apart in $1\,s$ . From what point above the upper point it began to fall?......... $m$ (Take $g = 10\,m\,s^{-2}$ )

Water is filled in a container upto height of $3\,m$. A small hole of area $‘A_0’$ is punched in the wall of the container at a height $52.5\, cm$ from the bottom. The cross sectional area of the container is $A$. If $A_0/A = 0.1$ then $v^2$ is......... $m^2/s^2$ (where $v$ is the velocity of water coming out of the hole)

The adjacent figure is the part of a horizontally stretched net. section $AB$ is stretched with a force of $10 \,N$. The tensions in the sections $BC$ and $BF$ are

A transverse wave propagating along $X-$axis is represented by
$\text{y}(\text{x,t})=8.0\sin\Big(0.5\pi\text{x}-4\pi\text{t}-\frac{\pi}{4}\Big)$
where $x$ is in metre and $t$ is in seconds. The speed of the wave is:

Which of the following time measuring devices is most precise?

The diagram to the right shows the velocity-time graph for two masses $R$ and $S$ that collided elastically. Which of the following statements is true?

$(I)$ $R$ and $S$ moved in the same direction after the collision.

$(II)$ Kinetic energy of the system $(R$ & $S)$ is minimum at $t = 2$ milli sec.

$(III)$ The mass of $R$ was greater than mass of $S.$