Relative Velocity in 2D

Q.

Two trains $120m$ and $80m$ in length are running in opposite directions with velocities $42km/hr$ and $30km/hr$ respectively. In what time will they completely pass each other.

Q.

Check the correctness of the equation wavelength = h/mv.

Q. The speed of a swimmer in still water is $20\text{m/s}$. The speed of river water is $10\text{m/s}$ and is flowing due east. If he is standing on the south bank and wishes to cross the river along the shortest path, the angle at which he should make his strokes with respect to the north, is given by

1. ${30}^{\circ }$ west
2. $0^{\circ }$ west
3. ${60}^{\circ }$ west
4. ${45}^{\circ }$ west

Q. A boat, which has a speed of $5km/h$ in still water, crosses a river of width $1km$ along the shortest possible path in $15\text{minutes}$. What is the magnitude of velocity of the river water?

1. $5km/h$
2. $3km/h$
3. $6km/h$
4. $4km/h$

Q. A river 400 m wide is flowing at a rate of $2\text{m/s}$. A boat is sailing at a velocity of 10.0 m/s with respect to the water, in a direction perpendicular to the river. Find the time (in seconds) taken by the person to reach the opposite bank at a point directly opposite to its starting point considering that after reaching the opposite bank, the person walks at $4\text{m/s}$ if needed to reach the point directly opposite to its starting point.

Q.

A heavy string of mass m hangs between two fixed points A and B at the same level. The tangents to the string at A and B are at an angle $\theta$ with the horizontal as shown in the figure. The tension in the string at the lowest point is

1. $\frac{mg}{2sin\theta }$

2. $\frac{mg}{2cos\theta }$

3. $\frac{mg}{2tan\theta }$

4. $\frac{mg}{2cot\theta }$

Q. A swimmer wishes to cross a river $500m$ wide flowing at a rate $u$. His speed with respect to still water is $V$. For this, he makes an angle $\theta$ with the vertical to the direction of flow of the river as shown. In order to cross the river in minimum time, the value $\theta$ of in degrees should be

1. $0^{\circ }$
2. ${45}^{\circ }$
3. ${60}^{\circ }$
4. ${90}^{\circ }$

Q. A particle is projected at angle ${60}^{\circ }$ with speed $10\sqrt{3}\text{m/s}$ , from the point $‘A^{\prime }$ as shown in the figure. At the same time the wedge is made to move with speed $10\sqrt{3}\text{m/s}$ towards right as shown in the figure.Then, the time(in $s$) after which particle will strike the wedge is

Q. A jet airplane travelling at a speed of $500\text{km/h}$ ejects its products of combustion at the speed of $1500\text{km/h}$ relative to the jet plane. What is the speed of the latter with respect to an observer on the ground?

1. $500\text{km/h}$
2. $1000\text{km/h}$
3. $2000\text{km/h}$
4. $1500\text{km/h}$

Q. A motorboat going downstream overcomes a raft at a point A. 60 min later it turned back, and after some time it crossed the raft again at a distance $l=6$ km from point A. Then,

1. Flow velocity of river is 3 km/h.
2. Flow velocity of river is 4 km/h.
3. Velocity of motorboat is 6 km/h.
4. Velocity of motorboat is 9 km/h.

Q. A train is moving towards east and a car is moving along north, both with the same speed. The observed direction of car to the passenger in the train is

1. East – North direction
2. West – North direction
3. South – East direction
4. South – West direction

Q.

Six particles situated at the corners of a regular hexagon of side a move at a constant speed v. Each particle maintains a direction towards the particle at the next corner. Calculate the time the particles will take to meet each other.

1. 

2. 

3. 

4. 

Q. A train approaching a railway crossing at a speed of $120{\text{kmh}}^{-1}$ sounds a short whistle at frequency $640\text{Hz}$, when it is $300\text{m}$ away from the crossing. The speed of sound in air is $340{\text{ms}}^{-1}$. What will be frequency heard by a person standing on a road perpendicular to the track through the crossing at a distance of $400\text{m}$ from the crossing ?

1. $660\text{Hz}$
2. $680\text{Hz}$
3. $700\text{Hz}$
4. $720\text{Hz}$

Q. if ve is escape velocity for earth when projectile is fired from surface of earth , then escape velocity if same projectile is fired from earths centre

Q. Two cars $X$ and $Y$ are approaching each other with velocities $36\text{km/h}$ and $72\text{km/h}$ respectively. The frequency of a whistle sound as emitted by a passenger in car $X$, heard by the passenger in car $Y$ is $1320\text{Hz}$. If the velocity of sound in air is $340\text{m/s}$, the actual frequency of the whistle sound produced is $\text{Hz}$.

Q. A swimmer crosses the river along the line making an angle of ${45}^{\circ }$ with the direction of flow. Velocity of the river water is $5\text{m/s}$. Swimmer takes 6 seconds to cross the river of width $60\text{m}$. The magnitude of velocity of the swimmer with respect to river will be

1. $10\text{m/s}$
2. $12\text{m/s}$
3. $5\sqrt{5}\text{m/s}$
4. $10\sqrt{5}\text{m/s}$

Q.

A particle projected from point O with velocity u in a direction making an angle $\alpha$ with the horizontal. At any instant its position is at point P at right angles to the initial direction of projection. Its velocity at point O is

1. 

2. 

3. 

4. 

Q. Two particles $A$ and $B$ are projected simultaneously from the top of two towers of height $10\text{m}$ and $20\text{m}$ respectively. Particle $A$ is projected upwards at an angle of ${45}^{\circ }$ with horizontal at a speed of $10\sqrt{2}\text{m/s}$ and particle $B$ is projected horizontally at a speed of $10\text{m/s}$ towards $A$. What is the distance between towers if particles collide in the air ?Take $g=10{\text{m/s}}^2$.

1. $10.5\text{m}$
2. $25\text{m}$
3. $35\text{m}$
4. $20\text{m}$

Q. Two ships are 10 km apart on a line joining south to north. The one farther north is steaming west at $20{\text{km h}}^{-1}$. The other is steaming north at $20{\text{km h}}^{-1}$. What is their distance of closest approach? How long do they take to reach it?

1. $5\sqrt{2}\text{km},15\text{min}$
2. $10\text{km},12\text{min}$
3. $5\sqrt{2}\text{km},12\text{min}$
4. $5\sqrt{2}\text{km},10\sqrt{2}\text{min}$

Q.

Which one of the following graphs shows the variation of acceleration due to gravity with depth h from the surface:

1. 

2. 

3. 

4. 

Q. A man wants to cross the river to an exactly opposite point on the other bank. If he can row his boat with twice the velocity of the current, then at what angle to the current he must keep the boat pointed?

1. ${90}^{\circ }$
2. ${120}^{\circ }$
3. ${150}^{\circ }$
4. ${60}^{\circ }$

Q. For an observer on trolley, direction of projection of particle is shown in the figure, while for observer on ground ball rise vertically. The maximum height reached by ball from trolley is (take $g=10m/s^2$)

1. $10m$
2. $15m$
3. $20m$
4. $5m$

Q. A fighter plane, flying horizontally with a speed of 360 $km/h$ at an altitude of 500 $m$ drops a bomb for a target straight ahead of it on the ground. At what approximate distance, the bomb should be dropped ahead of the target, so that it hits the target ? Assume that acceleration due to gravity, $g$ is $10m{s}^{-2}$. Also neglect air drag.

1. 866 $m$
2. $50\sqrt{5}m$
3. $500\sqrt{5}m$
4. 1000 $m$

Q.

A train 50 m long passes over a bridge 250 m long at a velocity of 30 km/h. How long will it take to completely pass over the bridge?

Q. A man can row a boat at $4\text{km/hr}$ in still water. He is crossing a river where the current velocity is $2\text{km/hr}$ . In what direction should his boat be headed if he wants to reach a point on the other bank, directly opposite to the starting point?

1. ${120}^{\circ }$ with the direction of flow
2. ${150}^{\circ }$ with the direction of flow
3. ${60}^{\circ }$ with the direction of flow
4. ${90}^{\circ }$ with the direction of flow

Q. In the given figure, a particle $A$ moves along the line $y=30\text{m}$ with a constant velocity of magnitude $3\text{m/s}$ and parallel to the $x-$ axis. At the instant particle $A$ passes the $y-$ axis, the particle $B$ leaves the origin with a zero initial speed and a constant acceleration of magnitude $0.40{\text{m/s}}^2$. What angle $\theta$ between${\overrightarrow{a}}_B$ and the positive direction of the $y-$axis would result in a collision?

1. ${15}^{\circ }$
2. ${30}^{\circ }$
3. ${45}^{\circ }$
4. ${60}^{\circ }$

Q. A cart is moving horizontally along a straight line with constant speed $30{\text{ms}}^{-1}$. A particle is to be fired vertically upwards from the moving cart in such a way that it returns to the cart at the same point from where it was projected after the cart has moved $80\text{m}$. At what speed (relative to the must the projectile be fired? (Take $g=10{\text{ms}}^{-2}$)

1. $10\sqrt{8}{\text{ms}}^{-1}$
2. $\frac{40}{3}{\text{ms}}^{-1}$
3. none of these
4. $10{\text{ms}}^{-1}$

Q. A boat man could row his boat with a speed $10\text{m/sec}$. He wants to take his boat from $P$ to a point $Q$ just opposite on the other bank of the river flowing at a speed $4\text{m/sec}$. He should row his boat–

1. At right angle to the stream
2. At an angle of ${\sin }^{–1}\left(\frac{2}{5}\right)$ with $PQ$ up the stream
3. At an angle of ${\sin }^{–1}\left(\frac{2}{5}\right)$ with $PQ$ down the stream
4. At an angle of ${\cos }^{–1}\left(\frac{2}{5}\right)$ with $PQ$ down the stream

Q. A boat moves with a speed of $5km/h$ relative to water in a river flowing with a speed of $3km/h$ and having a width of $1km$. The time taken in a round trip, when boat travel shortest distance is

1. $5min$
2. $60min$
3. $20min$
4. $30min$

Q. A train $S_1$ moving with a uniform velocity of $108km/h$ approaches another train $S_2$ standing on a platform. An observer $O$ moves with a uniform velocity of $36km/h$ towards $S_2$ as shown in figure. Both the trains are blowing whistles of same frequency $120Hz$. When O is $600m$ away from $S_2$ and distance between $S_1$ and $S_2$ is $800m$, the number of beats heard by O is . (Speed of the sound $=330m/s$)