The position vector of the particle is r t = a cos ⁡ ω t i ^ + a sin ⁡ ω t j ^ , where a and ω are real constants of suitable dimensions. The acceleration is

Perpendicular to the position vector

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Velocity of the particle changes from $\vec{v_{1}} = 2 \hat{i} + 3 \hat{j} (m / s) to \vec{v_{2}} = 10 \hat{i} + 9 \hat{j} (m / s) in 5 s$ . Then the magnitude of change in velocity would be

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Important Questions on Motion in a Plane

EASY

Science>Physics>Motion in a Plane>Motion in Two Dimensions

A football player is moving southward and suddenly turns eastward with the same speed to avoid an opponent. The force that acts on the player while turning is :

MEDIUM

Science>Physics>Motion in a Plane>Motion in Two Dimensions

Two bodies were thrown simultaneously from the origin: one straight up and the other, at an angle,

60 °

to the vertical. The initial velocity of each body is equal to

10 m s^{- 1}

Neglecting the air resistance, the distance between the two bodies after

t = 2 s

is (

Use g = 10 m s^{- 2}

)

EASY

Science>Physics>Motion in a Plane>Motion in Two Dimensions

At time

t = 0

a particle starts travelling from a height

7 \hat{z} cm

in a plane keeping

z

coordinate constant. At any instant of time, it's position along the

x

and

y

directions are defined as

3 t

and

5 t^{3}

respectively. At

t = 1 s

acceleration of the particle will be

EASY

Science>Physics>Motion in a Plane>Motion in Two Dimensions

A person walks

25 °

north of east for

3.18 km

. How far would she have to walk due north and then due east to arrive at the same location?

EASY

Science>Physics>Motion in a Plane>Motion in Two Dimensions

A mosquito is moving with a velocity $\vec{v} = 0.5 t^{2} \hat{i} + 3 t \hat{j} + 9 \hat{k} m s^{- 1}$ and accelerating in uniform conditions. What will be the direction of mosquitoes after $2 s$ ?

EASY

Science>Physics>Motion in a Plane>Motion in Two Dimensions

The position vector of the particle is

r (t) = a \cos ω t \hat{i} + a \sin ω t \hat{j}

, where

a

and

ω

are real constants of suitable dimensions. The acceleration is

MEDIUM

Science>Physics>Motion in a Plane>Motion in Two Dimensions

The y-component of vector

\vec{A}

+ 3.0 m

. If A makes an angle of

30 °

counter-clockwise from the positive

y

- axis, the magnitude of

\vec{A}

is (assume

\vec{A}

is in

x - y

plane)

EASY

Science>Physics>Motion in a Plane>Motion in Two Dimensions

t = 0,

a particle starts moving from the origin with the velocity,

5.01 m s^{- 1}

, it moves in

x - y

plane due to a force having a constant acceleration of

(2.0 \hat{i} + 3.0 \hat{j}) m s^{- 2}

. Find the coordinate of the particle at

t = 6 s

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Science>Physics>Motion in a Plane>Motion in Two Dimensions

A butterfly is flying with a velocity

4 \sqrt{2} m s^{- 1}

in north-east direction. Wind is slowly blowing at

1 m s^{- 1}

from north to south. The resultant displacement of the butterfly in

3

seconds is:

EASY

Science>Physics>Motion in a Plane>Motion in Two Dimensions

A bird flies at an angle of

60 °

to the horizontal. Its horizontal component of velocity is

10 m / s

. Find its vertical component of velocity in

m / s

HARD

Science>Physics>Motion in a Plane>Motion in Two Dimensions

Three balls, $A, B$ and $C$ are released and all reach the point $X$ (shown in the figure). Balls $A$ and $B$ are released from two identical structures, one kept on the ground and the other at height $h$ from the ground as shown in the figure. They take time $t_{A}$ and $t_{B}$ respectively to reach $X$ (time starts after they leave the end of the horizontal portion of the structure). The ball $C$ is released from a point at height $h$ vertically above $X$ and reaches $X$ in time $t_{C}$ . Choose the correct statement.

Question Image

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Science>Physics>Motion in a Plane>Motion in Two Dimensions

A balloon is moving up in air vertically above a point $A$ on the ground. When it is a height $h_{1},$ a girl standing at a distance d (point B) from A (see figure) sees it at an angle $45 °$ with respect to the vertical. When the balloon climbs up a further height $h_{2}$ , it is seen at an angle $60 °$ with respect to the vertical if the girl moves further by a distance $2.464 d$ (point C). Then the height $h_{2}$ is (given $\tan 30 ° = 0.5774$ ):

Question Image

HARD

Science>Physics>Motion in a Plane>Motion in Two Dimensions

A particle starts from the origin at

t = 0 s

with a velocity of

10 \hat{j} m s^{- 1}

and move in the

x - y

plane with a constant acceleration of

(8 \hat{i} + 2 \hat{j}) m s^{- 2}

. At an instant when the

x -

coordinate of the particle is

16 m, y

-coordinate of the particle is:

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Science>Physics>Motion in a Plane>Motion in Two Dimensions

A ball is thrown horizontally from a height with a certain initial velocity at time

t = 0

. The ball bounces repeatedly from the ground with the coefficient of restitution less than

1

as shown.

Neglect air resistance and taking the upward direction as positive, which figure qualitatively depicts the vertical component of the ball's velocity

(v_{y})

as a function of time

(t)

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Science>Physics>Motion in a Plane>Motion in Two Dimensions

A particle moves over a

x y

plane with a constant acceleration

\vec{a} = (4.0 m s^{- 2}) \hat{i} + (4.0 m s^{- 2} \hat{j})

. At the time

t = 0,

the velocity is

(4.0 m s^{- 2}) \hat{i} .

The speed of the particle when it is displaced by

6.0 m

parallel to the

x

-axis is,

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Science>Physics>Motion in a Plane>Motion in Two Dimensions

A car P is moving with a uniform speed

72 km {hr}^{- 1}

towards another car Q at rest on a straight level road. At a particular instance when the distance between P and Q is

525 m

the car Q started accelerating at

2 {ms}^{- 2}

towards P. Find the distance travelled by Q, when both the cars meet.

EASY

Science>Physics>Motion in a Plane>Motion in Two Dimensions

A particle leaves the origin with initial velocity

\vec{v} = (3 \hat{i}) m s^{- 1}

and a constant acceleration

\vec{a} = (- 1 \hat{i} - 0.5 \hat{j}) m s^{- 2}

. The position vector of particle, when it reaches its maximum

x

-coordinate, is

EASY

Science>Physics>Motion in a Plane>Motion in Two Dimensions

A particle is moving in

x y

-plane crosses the origin at time

t = 0 .

The equation of motion of the particle is

y = 4 x^{2} .

If the velocity of the particle is

\vec{v} = (2 \hat{i} + 2 \hat{j}) m s^{- 1}

and acceleration is

\vec{a} = (a \hat{j}) m s^{- 2}

, then the magnitude of

a

MEDIUM

Science>Physics>Motion in a Plane>Motion in Two Dimensions

A particle moving in a gravity free space along horizontal with a velocity

1 m s^{- 1}

is subjected to an acceleration

(2 \hat{i} + 4 \hat{j}) m s^{- 2}

. Then the vertical distance covered by the particle by the time it covers a horizontal distance

6 m

MEDIUM

Science>Physics>Motion in a Plane>Motion in Two Dimensions

A particle starts from the origin at

t = 0

with an initial velocity of

(3.0 \hat{i}) m s^{- 1}

and moves in the

x - y

plane with a constant acceleration

(6.0 \hat{i} + 4.0 \hat{j}) m s^{- 2}

. The

x -

coordinate of the particle at the instant when its

y -

coordinate is

32 m

D

meters. The value of

D

is:

Velocity of the particle changes from v1→=2i^+3j^ (m/s) to v2→=10i^+9j^ (m/s) in 5 s. Then the magnitude of change in velocity would be

Important Questions on Motion in a Plane

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Velocity of the particle changes from $\vec{v_{1}} = 2 \hat{i} + 3 \hat{j} (m / s) to \vec{v_{2}} = 10 \hat{i} + 9 \hat{j} (m / s) in 5 s$ . Then the magnitude of change in velocity would be