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An inclined plane making an angle $β$ with horizontal. A projectile projected from the bottom of the plane with a speed u at angle $α$ with horizontal, then its maximum range $R_{m a x}$ is

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Important Questions on Motion in a Plane

MEDIUM

Physics>Mechanics>Motion in a Plane>Projectile Motion

A projectile is given an initial velocity of

(\hat{i} + \sqrt{3} \hat{j}) m s^{- 1},

where

\hat{i}

is along the ground and

\hat{j}

is along the vertical. Then, the equation of the path of projectile is

[

Take,

g = 10 m s^{- 2}]

EASY

Physics>Mechanics>Motion in a Plane>Projectile Motion

At what angle

θ

to the horizontal should an object is projected so that the maximum height reached is equal to the horizontal range?

MEDIUM

Physics>Mechanics>Motion in a Plane>Projectile Motion

A stone is projected with velocity

2 \sqrt{g h}

, so that it just clears two walls of equal height

h

, at distance of

2 h

from each other. The time interval of passing between the two walls is

EASY

Physics>Mechanics>Motion in a Plane>Projectile Motion

A man of height

7.33 ft

releases a stone from the slingshot just above his head. If the stone travels in a vertical direction towards the sky with velocity of

10 m s^{- 1}

, then the time it takes to reach the ground is (Assume acceleration due to gravity

g = 10 m s^{- 2}

)

EASY

Physics>Mechanics>Motion in a Plane>Projectile Motion

Which of the following graphs represents the speed

v

of a vertical projectile as a function of time

t

MEDIUM

Physics>Mechanics>Motion in a Plane>Projectile Motion

A ball is dropped from a height

H

from rest. The ball travels

\frac{H}{2}

in last

1.0 s

. The total time taken by the ball to hit the ground is

MEDIUM

Physics>Mechanics>Motion in a Plane>Projectile Motion

An aeroplane is flying in a horizontal direction with a velocity

u

and at a height of

2000 m

. When it is vertically below a point

A

on the ground a food packet is released from it. The packet strikes the ground at point

B

. If

A B = 3 km

and

g = 10 m s^{- 2}

, then the value of

u

MEDIUM

Physics>Mechanics>Motion in a Plane>Projectile Motion

Two long parallel plates $A$ and $B$ are separated by a distance of $4 cm$ with an electric field of $45.5 V m^{- 1}$ between the plates directed normally from plate $A$ to plate $B,$ as shown in the figure. An electron is projected from plate $A$ with velocity $v$ at an angle of $30 °$ with the surface of plate $A$ . The maximum value of $v$ so that the electron does not hit plate $B$ is
$($ Assume gravity free space, charge of electron $= 1.6 \times 10^{- 19} C$ and mass of electron $= 9.1 \times 10^{- 31} kg)$

Question Image

EASY

Physics>Mechanics>Motion in a Plane>Projectile Motion

A boy is standing on top of a tower of height,

85 m

and throws a ball in the vertically upward direction with a certain speed. If

5.25 s

later he hears the ball hitting the ground, then the speed with which the boy threw the ball is (take

g = 10 m s^{- 2},

the speed of sound in air is

340 m s^{- 1}

)

MEDIUM

Physics>Mechanics>Motion in a Plane>Projectile Motion

The position of a projectile launched from the origin at t = 0 is given by

\vec{r} = (40 \hat{i} + 50 \hat{j}) m

at t = 2s. If the projectile was launched at an angle

θ

from the horizontal, then

θ

is (take g = 10 ms^-2).

HARD

Physics>Mechanics>Motion in a Plane>Projectile Motion

Two objects are located at height

10 m

above the ground. At some point of time, the objects are thrown with initial velocity

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

at an angle

45 °

and

135 °

with the positive

X

-axis respectively. Assuming

g = 10 m s^{- 2}

, the velocity vectors will be perpendicular to each other at time equal to

MEDIUM

Physics>Mechanics>Motion in a Plane>Projectile Motion

When an object is shot from the bottom of a long smooth inclined plane kept at an angle

60 °

with horizontal, it can travel a distance

x_{1}

along the plane. But, when the inclination is decreased to

30 °

and the same object is shot with the same velocity, it can travel

x_{2}

distance. Then

x_{1} : x_{2}

will be

EASY

Physics>Mechanics>Motion in a Plane>Projectile Motion

Two towers

A

and

B

, each of height

20 m

are situated a distance

200 m

apart. A body thrown horizontally from the top of the tower A with a velocity

20 {ms}^{- 1}

towards the tower

B

hits the ground at point

P

and another body thrown horizontally from the top of tower

B

with a velocity

30 {ms}^{- 1}

towards the tower A hits the ground at point

Q

. If a car starting from rest from

P

reaches

Q

10

seconds, the acceleration of the car is _________

(

Acceleration due to gravity

= 10 {ms}^{- 2})

EASY

Physics>Mechanics>Motion in a Plane>Projectile Motion

Two projectiles

A

and

B

are projected with the same initial speed.

A

is launched at an angle

ϕ

with the horizontal and

B

at an angle

ϕ

with the vertical. If

A

has a range

R_{1}

and

B

has a range

R_{2}

, then

EASY

Physics>Mechanics>Motion in a Plane>Projectile Motion

A body is projected horizontally from the top of a tower of height

180 m

with a velocity of

20 {ms}^{- 1}

. If acceleration due to gravity is

10 {ms}^{- 2}

then match the following.

List-I		List-II
$(A)$	Velocity of the body after $1$ second $($ in ${ms}^{- 1}$ )	(I)	$5$
$(B)$	Horizontal displacement of the body after $1$ second (in meters)	(ii)	$20$
$(C)$	Vertical displacement of the body after $1$ second (in meters)	(iii)	$10$
$(D)$	Vertical velocity of the body after $1$ second $($ in ${ms}^{- 1}$ )	(iv)	$22.4$

The correct answer is

HARD

Physics>Mechanics>Motion in a Plane>Projectile Motion

Two particles are simultaneously projected in the horizontal direction from a point $P$ at a certain height. The initial velocities of the particles are oppositely directed to each other and have magnitude $v$ each. The separation between the particles at a time when their position vectors (drawn from the point $P)$ are mutually perpendicular, is:

HARD

Physics>Mechanics>Motion in a Plane>Projectile Motion

A projectile thrown with an initial velocity of $10 m s^{- 1}$ at an angle $α$ with the horizontal, has a range of $5 m .$ Taking $g = 10 m s^{- 2}$ and neglecting air resistance, what will be the estimated value of $α ?$

MEDIUM

Physics>Mechanics>Motion in a Plane>Projectile Motion

Two balls are projected at an angle

θ

and

(90 ° - θ)

with respect to the horizontal with the same speed. The ratio of their maximum vertical heights is

EASY

Physics>Mechanics>Motion in a Plane>Projectile Motion

A projectile is given an initial velocity of

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

, where

\hat{i}

is along the ground and

\hat{j}

is along the vertically upward direction. If

g = 10 m s^{- 2}

, the equation of its trajectory is :

HARD

Physics>Mechanics>Motion in a Plane>Projectile Motion

A plane is inclined at an angle

α = 30 °

with respect to the horizontal. A particle is projected with a speed

u = 2 m s^{- 1}

, from the base of the plane, making an angle

θ = 15 °

with respect to the plane as shown in the figure. The distance from the base, at which the particle hits the plane is close to:
(Take

g = 10 m s^{- 2}

)

An inclined plane making an angle β with horizontal. A projectile projected from the bottom of the plane with a speed u at angle α with horizontal, then its maximum range Rmax is

Important Questions on Motion in a Plane

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An inclined plane making an angle $β$ with horizontal. A projectile projected from the bottom of the plane with a speed u at angle $α$ with horizontal, then its maximum range $R_{m a x}$ is