Relative Velocity

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JEE Main 2020, 2 Sep Shift-I

LEVELJEE Main

Trains $A$ and $B$ are running on parallel tracks in the opposite directions with speeds of $36 km/h$ and $72 km/h$ , respectively. A person is walking in train $A$ in the opposite direction to its motion with a speed of $1.8 km/h$ . Speed (in $ms^{- 1}$ ) of this person as observed from train $B$ will be close to (Take, the distance between the tracks as negligible)

JEE Main 2020, 8 Jan Shift-I

LEVELJEE Main

A particle is moving along the $x$ -axis with its coordinate with the $t$ given by $x (t) = 10 + 8 t - 3 t^{2}$ . Another particle is moving along the $y$ -axis with its coordinate as a function of time given by $y (t) = 5 - 8 t^{3}$ . At $t = 1 s$ , the speed of the second particle as measured in the frame of the first particle is given as $v$ . Then $v$ (in m/s) is ......... .

JEE Main 2019, 8 April Shift-I

LEVELJEE Advanced

Ship A is sailing towards north-east with velocity $v = 30 \hat{i} + 50 \hat{j}$ km/h, where $\hat{i}$ points east and $\hat{j}$ north. Ship B is at a distance of 80 km east and 150 km north of Ship A and is sailing towards west at 10 km/h. A will be at minimum distance from B in

JEE Main 2021, 16 March Shift-II

LEVELJEE Main

A swimmer can swim with velocity of $12 km/h$ in still water. Water flowing in a river has velocity $6 km/h$ . The direction with respect to the direction of flow of river water he should swim in order to reach the point on the other bank just opposite to his starting point is ……… $^{\circ}$ (in degree). (Round off to the nearest integer)

JEE Main 2021 (27 July Shift-II)

LEVELJEE Main

A swimmer wants to cross a river from point $A$ to point $B$ . Line $A B$ makes an angle of $3 0^{\circ}$ with the flow of river. Magnitude of velocity of the swimmer is same as that of the river. The angle $θ$ with the line $A B$ should be ...... $^{\circ}$ , so that the swimmer reaches point $B$ .

JEE Main 2021, 20 July Shift-I

LEVELJEE Main

A butterfly is flying with a velocity $42$ m/s in North-East direction. Wind is slowly blowing at 1 m/s from North to South. The resultant displacement of the butterfly in 3 s is

122

(D)

15 m

JEE Main 2019, 12 Jan Shift-I

LEVELJEE Main

A passenger train of length $60 m$ travels at a speed of $80 km/hr$ . Another freight train of length $120 m$ travels at a speed of $30 km/hr$ . The ratio of times taken by the passenger train to completely cross the freight train when : (i) they are moving in the same direction and (ii) in the opposite direction is

(A)

\frac{3}{2}

(B)

\frac{25}{11}

(C)

\frac{11}{5}

(D)

\frac{5}{2}

JEE Main 2020, 6 Sep Shift-II

LEVELJEE Advanced

When a car is at rest, its driver sees rain drops falling on it vertically. When driving the car with speed $v$ , he sees that rain drops are coming at an angle $6 0^{\circ}$ from the horizontal. On further increasing the speed of the car to $(1 + β) v$ , this angle changes to $4 5^{\circ}$ . The value of $β$ is close to

JEE Main 2021, 18 March Shift-I

LEVELJEE Main

A person is swimming with a speed of $10 m/s$ at an angle of $12 0^{\circ}$ with the flow and reaches to a point directly opposite on the other side of the river. The speed of the flow is $x m/s$ . The value of $x$ to the nearest integer is ……… .

JEE Main 2021, 26 Aug Shift-II

LEVELJEE Main

A bomb is dropped by fighter plane flying horizontally. To an observer sitting in the plane, the trajectory of the bomb is a

(A)

hyperbola

(B)

parabola in the direction of motion of plane

(C)

straight line vertically down the plane

(D)

parabola in a direction opposite to the motion of plane

JEE Main 2019, 9 April Shift-I

LEVELJEE Main

The stream of a river is flowing with a speed of $2 km/h$ . A swimmer can swim at a speed of $4 km/h$ . What should be the direction of the swimmer with respect to the flow of the river to cross the river straight ?

(A)

6 0^{\circ}

(B)

12 0^{\circ}

(C)

9 0^{\circ}

(D)

15 0^{\circ}

JEE Main 2021, 20 July Shift-II

LEVELJEE Main

A boy reaches the airport and finds that the escalator is not working. He walks up the stationary escalator in time $t_{1}$ . If he remains stationary on a moving escalator, then the escalator takes him up in time $t_{2}$ . The time taken by him to walk up on the moving escalator will be

(A)

\frac{t _{1} t _{2}}{t _{2} - t _{1}}

(B)

\frac{t _{1} + t _{2}}{2}

(C)

\frac{t _{1} t _{2}}{t _{2} + t _{1}}

(D)

t_{2} - t_{1}

JEE Main 2015

LEVELJEE Advanced

Two stones are thrown up simultaneously from the edge of a cliff 240 m high with initial speed of 10 m/s and 40 m/s respectively. Which of the following graph best represents the time variation of relative position of the second stone with respect to the first? Assume stones do not rebound after hitting the ground and neglect air resistance, take $g = 10 m/s^{2}$ )

A particle of mass $m$ , moving in a circular path of radius $R$ with a constant speed $v_{2}$ is located at point $(2 R, 0)$ at time $t = 0$ and a man starts moving with a velocity $v_{1}$ along the positive Y-axis from origin at time $t = 0$ . Calculate the linear momentum of the particle w.r.t. man as a function of time.

JEE Advanced 2011

LEVELJEE Advanced

A train is moving along a straight line with a constant acceleration $a$ . A boy standing in the train throws a ball forward with a speed of $10 m/s$ , at an angle of $6 0^{\circ}$ to the horizontal. The boy has to move forward by $1.15 m$ inside the train to catch the ball back at the initial height. The acceleration of the train, in $m/s^{2}$ , is.

JEE Advanced 1988

LEVELJEE Advanced

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 $15 min$ . The velocity of the river water in km/h is

(A)

1

(B)

3

(C)

4

(D)

41

JEE Advanced 1983

LEVELJEE Main

A river is flowing from West to East at a speed of $5 m/min$ . A man on the South bank of the river, capable of swimming at $10 m/min$ in still water, wants to swim across the river in the shortest time. He should swim in a direction

(A)

due North

(B)

3 0^{\circ}

East of North

(C)

3 0^{\circ}

West of North

(D)

6 0^{\circ}

East of North

JEE Advanced 2002

LEVELJEE Main

On a frictionless horizontal surface, assumed to be the $x$ - $y$ plane, a small trolley $A$ is moving along a straight line parallel to the $y$ -axis (see figure) with a constant velocity of $(3 - 1) m/s$ . At a particular instant when the line $O A$ makes an angle of $4 5^{\circ}$ with the $x$ -axis, a ball is thrown along the surface from the origin $O$ . Its velocity makes an angle $ϕ$ with the $x$ -axis and it hits the trolley. (2002) (a) The motion of the ball is observed from the frame of the trolley. Calculate the angle $θ$ made by the velocity vector of the ball with the $x$ -axis in this frame. (b) Find the speed of the ball with respect to the surface, if $ϕ = 4 θ /3$ .

JEE Advanced 1998

LEVELJEE Advanced

A large heavy box is sliding without friction down a smooth plane of inclination $θ$ . From a point $P$ on the bottom of the box, a particle is projected inside the box. The initial speed of the particle with respect to the box is $u$ and the direction of projection makes an angle $α$ with the bottom as shown in the figure. (a) Find the distance along the bottom of the box between the point of projection $P$ and the point $Q$ where the particle lands (Assume that the particle does not hit any other surface of the box. Neglect air resistance.) (b) If the horizontal displacement of the particle as seen by an observer on the ground is zero, find the speed of the box with respect to the ground at the instant when the particle was projected.

JEE Advanced 2008

LEVELJEE Main

Assertion For an observer looking out through the window of a fast moving train, the nearby objects appear to move in the opposite direction to the train, while the distant objects appear to be stationary. Reason If the observer and the object are moving at velocities $v_{1}$ and $v_{2}$ , respectively with reference to a laboratory frame, the velocity of the object with respect to the observer is $v_{2} - v_{1}$ .

(A)

If Assertion is true, Reason is true; Reason is the correct explanation for Assertion

(B)

If Assertion is true, Reason is true; Reason is not a correct explanation for Assertion

(C)

If Assertion is true; Reason is false

(D)

If Assertion is false; Reason is true

JEE Advanced 2014

LEVELJEE Advanced

Airplanes $A$ and $B$ are flying with constant velocity in the same vertical plane at angles $3 0^{\circ}$ and $6 0^{\circ}$ with respect to the horizontal respectively as shown in figure. The speed of $A$ is $1003 ms^{- 1}$ . At time $t = 0 s$ , an observer in $A$ finds $B$ at a distance of $500 m$ . This observer sees $B$ moving with a constant velocity perpendicular to the line of motion of $A$ . If at $t = t_{0}$ , $A$ just escapes being hit by $B$ , $t_{0}$ in seconds is

JEE Advanced 1994

LEVELJEE Advanced

Two towers $A B$ and $C D$ are situated a distance $d$ apart as shown in figure. $A B$ is $20 m$ high and $C D$ is $30 m$ high from the ground. An object of mass $m$ is thrown from the top of $A B$ horizontally with a velocity of $10 m/s$ towards $C D$ . Simultaneously, another object of mass $2 m$ is thrown from the top of $C D$ at an angle of $6 0^{\circ}$ to the horizontal towards $A B$ with the same magnitude of initial velocity as that of the first object. The two objects move in the same vertical plane, collide in mid-air and stick to each other. (1994) (a) Calculate the distance $d$ between the towers. (b) Find the position where the objects hit the ground.

JEE Advanced 1984

LEVELJEE Main

Four persons $K, L, M, N$ are initially at the four corners of a square of side $d$ . Each person now moves with a uniform speed $v$ in such a way that $K$ always moves directly towards $L$ , $L$ directly towards $M$ , $M$ directly towards $N$ and $N$ directly towards $K$ . The four persons will meet at a time ......

Pathfinder for Olympiad and JEE Advanced Physics

LEVELJEE Advanced

When a deer was 48 m from a leopard, the leopard starts chasing the deer and the deer immediately starts running away from the leopard with constant velocity. A leopard cannot run at high speeds for a long time and has to slow down due to fatigue. If we assume that the leopard starts with an initial speed of 30 m/s and reduces its speed in equal steps of 5 m/s after every 2 s interval, at what minimum speed must the deer run to escape from the leopard?

Pathfinder for Olympiad and JEE Advanced Physics

LEVELJEE Advanced

Two motorboats that can move with velocities 4.0 m/s and 6.0 m/s relative to water are going up-stream in a river. When the faster boat overtakes the slower boat, a buoy is dropped from the slower boat. After lapse of a time interval, both the boats turn back simultaneously and move at the same speeds relative to the water as before. Their engines are switched off when they reach the buoy again. If the maximum separation between the boats is 200 m after the buoy is dropped and water flow velocity in the river is 1.5 m/s, find distance between the places where the faster boat passes by the buoy.

A bomb is dropped by fighter plane flying horizontally. To an observer sitting in the plane, the trajectory of the bomb is a

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } 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 min. The velocity of the river water in km/h is

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 $15 min$ . The velocity of the river water in km/h is