Two particles A and B move with constant velocities v → 1 and v → 2 . At the initial moment their position vectors are r → 1 and r → 2 respectively. The condition for particles A and B for their collision is:

r → 1 - r → 2 r → 1 - r → 2 = v → 2 - v → 1 v → 2 - v → 1

r → 1 ⋅ v → 1 = r → 2 ⋅ v → 2

r → 1 × v → 1 = r → 2 × v → 2

r → 1 - r → 2 = v → 1 - v → 2

EASY

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A particle moves along a straight line $O X$ . At a time $t$ (in seconds) the distance $x$ (in meters) of the particle from $O$ is given by $x = 40 + 12 t - t^{3} .$ How long would the particle travel before coming to rest?

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Important Questions on Motion in a Plane

EASY

Physics>Mechanics>Motion in a Plane>Relative Velocity

Two particles A and B move with constant velocities

{\vec{v}}_{1}

and

{\vec{v}}_{2}

. At the initial moment their position vectors are

{\vec{r}}_{1}

and

{\vec{r}}_{2}

respectively. The condition for particles A and B for their collision is:

EASY

Physics>Mechanics>Motion in a Plane>Relative Velocity

The stream of a river is flowing with a speed of

2 k m h^{- 1}

. A swimmer can swim at a speed of

4 km h^{- 1}

. The direction of the swimmer with respect to the flow of the river, to cross the river straight, is

EASY

Physics>Mechanics>Motion in a Plane>Relative Velocity

Train

A

and train

B

are running on parallel tracks in the opposite directions with speed of

36 km {hour}^{- 1}

and

72 km {hour}^{- 1}

, respectively. A person is walking in train

A

in the direction opposite to its motion with a speed of

1.8 km {hour}^{- 1}

. Speed

(in m s^{- 1})

of this person as observed from train

B

will be close to: (take the distance between the tracks as negligible)

MEDIUM

Physics>Mechanics>Motion in a Plane>Relative Velocity

A person standing on an open ground hears the sound of a jet aeroplane, coming from north at an angle

60^{o}

with ground level, but he finds the aeroplane right vertically above his position. If

v

is the speed of sound, speed of the plane is:

EASY

Physics>Mechanics>Motion in a Plane>Relative Velocity

A car is standing

200 m

behind a bus, which is also at rest. The two start moving at the same instant but with different forward accelerations. The bus has acceleration

2 m s^{- 2}

and the car has acceleration

4 m s^{- 2}

. The car will catch up with the bus after time :

EASY

Physics>Mechanics>Motion in a Plane>Relative Velocity

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 coming at an angle

60^{\circ}

from the horizontal. On further increasing the speed of the car to

(1 + β) v

, this angle changes to

45^{\circ}

. The value of

β

is close to :

MEDIUM

Physics>Mechanics>Motion in a Plane>Relative Velocity

In U.C.M., when time interval

δ \to 0

, the angle between change in velocity

(δ v)

and linear velocity (

v

) will be

MEDIUM

Physics>Mechanics>Motion in a Plane>Relative Velocity

A ball is dropped from a bridge that is

45 m

above the water. It falls directly into a boat which is moving with constant velocity. The boat is

12 m

away from the point of impact when the ball is dropped. The speed of the boat is (Take

g = 10 m s^{- 2}

)

MEDIUM

Physics>Mechanics>Motion in a Plane>Relative Velocity

Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time

t_{1}

. On other days, if she remains stationary on the moving escalator, then the escalator takes her up in time

t_{2}

. The time taken by her to walk up on the moving escalator will be

MEDIUM

Physics>Mechanics>Motion in a Plane>Relative Velocity

The speed of a swimmer in still water is

20 m s^{- 1} .

The speed of river water is

10 m s^{- 1}

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

MEDIUM

Physics>Mechanics>Motion in a Plane>Relative Velocity

A person swims in a river aiming to reach exactly on the opposite point on the bank of a river. His speed of swimming is

0.5 m s^{- 1}

at an angle of

120 °

with the direction of flow of water. The speed of water is

MEDIUM

Physics>Mechanics>Motion in a Plane>Relative Velocity

A ship

A

is moving Westwards with a speed of

10 k m h^{- 1}

and a ship

B

100 km

south of

A

, is moving Northwards with a speed of

10 k m h^{- 1}

. The time after which the distance between them becomes shortest, is:

EASY

Physics>Mechanics>Motion in a Plane>Relative Velocity

Rain is falling vertically with a speed of

12 m s^{- 1}

. A woman rides a bicycle with a speed of

12 m s^{- 1}

in east to west direction. What is the direction in which she should hold her umbrella?

HARD

Physics>Mechanics>Motion in a Plane>Relative Velocity

Two stones are thrown up simultaneously from the edge of a cliff

240 m

high with an initial speed of

10 m s^{- 1}

and

40 m s^{- 1}

respectively. Which of the following graph best represents the time variation of the 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 {ms}^{- 2}

)(the figure are schematic and not drawn to scale)

EASY

Physics>Mechanics>Motion in a Plane>Relative Velocity

At a metro station, a girl walks up a stationary escalator in

20 \sec

. If she remains stationary on the escalator, then the escalator take her up in

30 \sec

. The time take her up in

30 \sec

. The time taken by her to walk up on the moving escalator will be

HARD

Physics>Mechanics>Motion in a Plane>Relative Velocity

Object

A

moves uniformly with a constant speed

v

to reach object

B

, while

B

in turn moves rectilinearly with a uniform velocity of

u < v

. At the initial moment

v

is perpendicular to

u

and the positions are separated by a distance

l

. The object

A

meets the object

B

at time

t

. The value of

t

HARD

Physics>Mechanics>Motion in a Plane>Relative Velocity

A boy runs on a horizontal road with a speed of

4 m s^{- 1}

while it is raining. He sees that the rain is making an angle

θ

with the vertical while running from west to east. However, when he runs from east to west, the angle is

α

. The rain is pouring down at an angle

45 °

with the vertical and at a speed of

8 m s^{- 1}

as shown in the figure. The ratio

\frac{\tan θ}{\tan α}

is,

MEDIUM

Physics>Mechanics>Motion in a Plane>Relative Velocity

Ship

A

is sailing towards north-east with velocity)

\vec{v} = 30 \hat{i} + 50 \hat{j} km h^{- 1}

where

\hat{i}

points east and

\hat{j},

north. The ship

B

is at a distance of

80 k m

east and

150 k m

north of Ship

A

and is sailing towards the west at

10 k m h^{- 1} .

A

will be at the minimum distance from

B

in:

MEDIUM

Physics>Mechanics>Motion in a Plane>Relative Velocity

Two stones of mass

m_{1}

and

m_{2}

(such that

m_{1} > m_{2}

) are dropped

Δ t

time apart from the same height towards the ground. At a later time

t

the difference in their speed is

Δ V

and their mutual separation is

Δ S .

While both stones are in flight

MEDIUM

Physics>Mechanics>Motion in a Plane>Relative Velocity

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 directions is:

A particle moves along a straight line OX. At a time t (in seconds) the distance x (in meters) of the particle from O is given by x = 40+12t− t 3 . How long would the particle travel before coming to rest?

Important Questions on Motion in a Plane

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A particle moves along a straight line $O X$ . At a time $t$ (in seconds) the distance $x$ (in meters) of the particle from $O$ is given by $x = 40 + 12 t - t^{3} .$ How long would the particle travel before coming to rest?