# Relative Velocity in 2D

## Trending Questions

**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 m/s. The speed of river water is 10 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

- 30∘ west
- 0∘ west
- 60∘ west
- 45∘ west

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

- 5 km/h
- 3 km/h
- 6 km/h
- 4 km/h

**Q.**A river 400 m wide is flowing at a rate of 2 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 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 θ with the horizontal as shown in the figure. The tension in the string at the lowest point is

mg2 sin θ

mg2 cos θ

mg2 tan θ

mg2 cot θ

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

- 0∘
- 45∘
- 60∘
- 90∘

**Q.**A particle is projected at angle 60∘ with speed 10√3 m/s , from the point ‘A′ as shown in the figure. At the same time the wedge is made to move with speed 10√3 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 km/h ejects its products of combustion at the speed of 1500 km/h relative to the jet plane. What is the speed of the latter with respect to an observer on the ground?

- 500 km/h
- 1000 km/h
- 2000 km/h
- 1500 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,

- Flow velocity of river is 3 km/h.
- Flow velocity of river is 4 km/h.
- Velocity of motorboat is 6 km/h.
- 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

- East – North direction
- West – North direction
- South – East direction
- 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.

**Q.**A train approaching a railway crossing at a speed of 120 kmh−1 sounds a short whistle at frequency 640 Hz, when it is 300 m away from the crossing. The speed of sound in air is 340 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 m from the crossing ?

- 660 Hz
- 680 Hz
- 700 Hz
- 720 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 km/h and 72 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 Hz. If the velocity of sound in air is 340 m/s, the actual frequency of the whistle sound produced is

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

- 10 m/s
- 12 m/s
- 5√5 m/s
- 10√5 m/s

**Q.**

A particle projected from point O with velocity u in a direction making an angle α 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

**Q.**Two particles A and B are projected simultaneously from the top of two towers of height 10 m and 20 m respectively. Particle A is projected upwards at an angle of 45∘ with horizontal at a speed of 10√2 m/s and particle B is projected horizontally at a speed of 10 m/s towards A. What is the distance between towers if particles collide in the air ?Take g=10 m/s2.

- 10.5 m
- 25 m
- 35 m
- 20 m

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

- 5√2 km, 15 min
- 10 km, 12 min
- 5√2 km, 12 min
- 5√2 km, 10√2 min

**Q.**

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

**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?

- 90∘
- 120∘
- 150∘
- 60∘

**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=10 m/s2)

- 10 m
- 15 m
- 20 m
- 5 m

**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 10 ms−2. Also neglect air drag.

- 866 m
- 50√5 m
- 500√5 m
- 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 km/hr in still water. He is crossing a river where the current velocity is 2 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?

- 120∘ with the direction of flow
- 150∘ with the direction of flow
- 60∘ with the direction of flow
- 90∘ with the direction of flow

**Q.**In the given figure, a particle A moves along the line y=30 m with a constant velocity of magnitude 3 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 m/s2. What angle θ between→aB and the positive direction of the y−axis would result in a collision?

- 15∘
- 30∘
- 45∘
- 60∘

**Q.**A cart is moving horizontally along a straight line with constant speed 30 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 m. At what speed (relative to the must the projectile be fired? (Take g=10 ms−2)

- 10√8 ms−1
- 403 ms−1
- none of these
- 10 ms−1

**Q.**A boat man could row his boat with a speed 10 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 m/sec. He should row his boat–

- At right angle to the stream
- At an angle of sin–1(25) with PQ up the stream
- At an angle of sin–1(25) with PQ down the stream
- At an angle of cos–1(25) with PQ down the stream

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

- 5 min
- 60 min
- 20 min
- 30 min

**Q.**A train S1 moving with a uniform velocity of 108 km/h approaches another train S2 standing on a platform. An observer O moves with a uniform velocity of 36 km/h towards S2 as shown in figure. Both the trains are blowing whistles of same frequency 120 Hz. When O is 600 m away from S2 and distance between S1 and S2 is 800 m, the number of beats heard by O is