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

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A car on the cross road is moving towards east at a speed of $40 km / hr$ . Another car which is $1 km$ south of the crossing is approaching the crossing with the same speed. Their closest distance of approach will be

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Important Questions on Kinematics

EASY

Physics>Mechanics>Kinematics>Relative Velocity

A fighter jet is flying horizontally at a certain altitude with a speed of

200 {m s}^{- 1}

. When it passes directly overhead an anti-aircraft gun, a bullet is fired from the gun, at an angle

θ

with the horizontal, to hit the jet. If the bullet speed is

400 m s^{- 1}

, the value of

θ

will be _____

°

HARD

Physics>Mechanics>Kinematics>Relative Velocity

The time period of a particle $P$ moving along a circular path of radius $1 cm$ is $π s .$ Another particle $Q$ starts from rest at a point $A$ and travelling along a straight line path reaches the point $B$ in $2 s$ . If $A B = 12 cm$ and the particles $P$ and $Q$ are respectively at $D$ and $B$ at an instant shown in the figure, the acceleration of particle $Q$ with respect to particle $P$ is _______ $cm s^{- 2}$ . (Points $A, B, C, D$ and $O$ lie along the same straight line)

Question Image

HARD

Physics>Mechanics>Kinematics>Relative Velocity

Two boys are standing at ends

A

and

B

of a ground where

A B = 200 m .

The boy at

B

starts running in a direction perpendicular to

A B

with a speed of

6 m s^{- 1} .

The body at

A

starts simultaneously with a velocity of

10 m s^{- 1}

and catches the other at time '

t

' where the time '

t

' is

MEDIUM

Physics>Mechanics>Kinematics>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:

MEDIUM

Physics>Mechanics>Kinematics>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

HARD

Physics>Mechanics>Kinematics>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)

MEDIUM

Physics>Mechanics>Kinematics>Relative Velocity

Ship

A

is moving westwards with a speed of

20 km h^{- 1}

and another ship

B

which is at

200 km

south of

A

is moving Northwards with a speed of

10 km h^{- 1}

. The time after which the distance between them is shortest and the shortest distance between them are respectively

EASY

Physics>Mechanics>Kinematics>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 :

MEDIUM

Physics>Mechanics>Kinematics>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

HARD

Physics>Mechanics>Kinematics>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>Kinematics>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:

MEDIUM

Physics>Mechanics>Kinematics>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

EASY

Physics>Mechanics>Kinematics>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:

MEDIUM

Physics>Mechanics>Kinematics>Relative Velocity

A person of height

1.6 m

is walking away from a lamp post of height

4 m

along a straight path on the flat ground. The lamp post and the person are always perpendicular to the ground. If the speed of the person is

60 cm s^{- 1}

, the speed of the tip of the person’s shadow on the ground with respect to the person is _____

cm s^{- 1}

MEDIUM

Physics>Mechanics>Kinematics>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

EASY

Physics>Mechanics>Kinematics>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

MEDIUM

Physics>Mechanics>Kinematics>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

HARD

Physics>Mechanics>Kinematics>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

MEDIUM

Physics>Mechanics>Kinematics>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>Kinematics>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:

A car on the cross road is moving towards east at a speed of 40km/hr. Another car which is 1km south of the crossing is approaching the crossing with the same speed. Their closest distance of approach will be

Important Questions on Kinematics

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A car on the cross road is moving towards east at a speed of $40 km / hr$ . Another car which is $1 km$ south of the crossing is approaching the crossing with the same speed. Their closest distance of approach will be