Introduction to 2D Motion

Q. Two men are walking along a horizontal straight line in the same direction. The man in the front walks at a speed $2\text{m/s}$ and the man behind walks at a speed $4\text{m/s}$. A third man is standing at a height $24\text{m}$ above the same horizontal line such that all three men are in the same vertical plane. The two walking men are blowing identical whistles which emit sounds of frequency $2010\text{Hz}$. The speed of sound in air is $335\text{m/s}$. At the instant when the moving men are $14\text{m}$ apart, the stationary man is equidistant from them. The number of beats per second heard by the stationary man is

(give your answer as the nearest integer value)

Q. A person standing on open ground hears the sound of a jet airplane, coming from the north at an angle ${30}^{\circ }$ with the horizontal. But he finds the airplane vertically above his position. If $v$ is the speed of sound, then speed of the plane is

1. $\frac{\sqrt{3}}{2}v$
2. $v$
3. $\frac{2}{\sqrt{3}}v$
4. $\frac{v}{2}$

Q. Which of the following represents a 2D motion?

1. A ball thrown vertically upwards
2. Motion of a pendulum
3. A stone dropped from a cliff
4. All of these

Q. A person standing on open ground hears the sound of a jet airplane, coming from the north at an angle ${30}^{\circ }$ with the horizontal. But he finds the airplane vertically above his position. If $v$ is the speed of sound, then speed of the plane is

1. $\frac{\sqrt{3}}{2}v$
2. $v$
3. $\frac{2}{\sqrt{3}}v$
4. $\frac{v}{2}$

Q. Two sinusoidal plane waves same frequency having intensities $I_0$ and $4I_0$ are travelling in same direction. The resultant intensity at a point at which waves meet with a phase difference of zero radian is

1. $I_0$
2. $9I_0$
3. $5I_0$
4. $3I_0$

Q. Which of the following represents a 2D motion?

1. A ball thrown vertically upwards
2. Motion of a pendulum
3. A stone dropped from a cliff
4. All of these

Q. If the form of a sound wave traveling through air is
$s(x,t)=\left(6.0nm\right)\cos (kx+\left(3000rad/s\right)t+\varphi )$
how much time does any given air molecule along the path take to move between displacements $s=+2.0nm$ and $s=-2.0nm$?

Q. A man wishes to cross a river and come back to original position by swimming minimum distance. If the width of the river is 50 m, speed of river is 2 m/s and velocity of man with respect to river is 4 m/s, then time taken by man to come back to original position is

1. 
   $\frac{50}{\sqrt{3}}$ sec
2. 
   50$\sqrt{2}$ sec
3. 
   25 sec
4. 
   25$\sqrt{3}$ sec