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A particle projected at an angle $θ$ with the horizontal from the centre of the floor of a cylindrical room of radius $r$ returns to the point of projection after three elastic collisions with the walls and the ceiling. If the particle remains in air for time $T$ , find the speed of projection.

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Important Questions on Kinematics

HARD

Physics>Mechanics>Kinematics>Projectiles

A particle aimed at a target, projected at an angle

15 °

with the horizontal is short of the target by

10 m

. If the same particle projected at an angle of

45 °

with the horizontal then it is away from the target by

15

meters. The angle of projection to hit the target is

MEDIUM

Physics>Mechanics>Kinematics>Projectiles

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>Kinematics>Projectiles

Four projectiles are fired with the same velocities at angles

25 °, 40 °, 55 °

and

70 °

with the horizontal. The range of projectile will be largest for the one projected at angle _____.

HARD

Physics>Mechanics>Kinematics>Projectiles

Points

P, Q

and

R

are in a vertical line such that

P Q = Q R

. A ball at

P

is allowed to fall freely with zero initial speed. The ratio of the times of descent through

P Q

and

Q R

HARD

Physics>Mechanics>Kinematics>Projectiles

A ball is thrown from ground at an angle

θ

with horizontal and with an initial speed

u_{0} .

For the resulting projectile motion, the magnitude of average velocity of the ball up to the point when it hits the ground for the first time is

V_{1} .

After hitting the ground, ball rebounds at the same angle

θ

but with a reduced speed of

\frac{u_{0}}{α} .

Its motion continues for a long time as shown in figure. If the magnitude of average velocity of the ball for entire duration of motion is

0.8 V_{1},

the value of

α

is______

HARD

Physics>Mechanics>Kinematics>Projectiles

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>Kinematics>Projectiles

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}]

MEDIUM

Physics>Mechanics>Kinematics>Projectiles

M.S. Dhoni hits two cricket balls in the air in a

T - 20

match. Both the balls leave his bat at the same velocity but at different angles of

30 °

and

60 °

respectively. If one ignores air friction and wind velocity, which of the following statements is correct? (Angles are with respect to the horizontal)

MEDIUM

Physics>Mechanics>Kinematics>Projectiles

A shell is fired from a fixed artillery gun with an initial speed

u

such that it hits the target on the ground at a distance

R

from it. If

t_{1}

and

t_{2}

are the values of the time taken by it to hit the target in two possible ways, the product

t_{1} t_{2}

is:

MEDIUM

Physics>Mechanics>Kinematics>Projectiles

Two projectiles

P

and

Q

thrown with velocities

v

and

\frac{v}{2}

respectively have the same range. If

Q

is thrown at an angle of

15 °

to the horizontal,

P

must be thrown at an angle of

HARD

Physics>Mechanics>Kinematics>Projectiles

A wheel of radius

R

is trapped in a mud pit and spinning. As the wheel is spinning, it splashes mud blobs with initial speed

u

from various points on its circumference. The maximum height from the centre of the wheel, to which a mud blob can reach is

EASY

Physics>Mechanics>Kinematics>Projectiles

Which of the following graphs represents the speed

v

of a vertical projectile as a function of time

t

MEDIUM

Physics>Mechanics>Kinematics>Projectiles

Two seconds after projection, a projectile is moving at

30 °

above the horizontal, after one more second, it is moving horizontally. The initial speed of the projectile is (Take

g = 10 {ms}^{- 2})

EASY

Physics>Mechanics>Kinematics>Projectiles

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}

)

MEDIUM

Physics>Mechanics>Kinematics>Projectiles

The projectile motion of a particle of mass $5 g$ is shown in the figure.

Question Image

The initial velocity of the particle is $5 \sqrt{2} {ms}^{- 1}$ and the air resistance is assumed to be negligible. The magnitude of the change in momentum between the points $A$ and $B$ is $x \times 10^{- 2} {kgms}^{- 1}$ . The value of $x$ , to the nearest integer, is ___ .

EASY

Physics>Mechanics>Kinematics>Projectiles

The maximum range of a gun on horizontal plane is

16 km

. If

g = 10 {m s}^{- 2}

, then muzzle velocity of a shell is

MEDIUM

Physics>Mechanics>Kinematics>Projectiles

For a projectile motion, the angle between the velocity and acceleration is minimum and acute at

HARD

Physics>Mechanics>Kinematics>Projectiles

The horizontal range and maximum height attained by a projectile are

R

and

H

respectively. If a constant horizontal acceleration

a = \frac{g}{4}

is imparted to the projectile due to wind, then its horizontal range and maximum height will be

EASY

Physics>Mechanics>Kinematics>Projectiles

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}

)

HARD

Physics>Mechanics>Kinematics>Projectiles

A ball is projected from the ground at an angle of

45 °

with the horizontal surface. It reaches a maximum height of

120 m

and returns to the ground. Upon hitting the ground for the first time, it loses half of its kinetic energy. Immediately after the bounce, the velocity of the ball makes an angle of

30 °

with the horizontal surface. The maximum height it reaches after the bounce (in meters) is _____________.

A particle projected at an angle θ with the horizontal from the centre of the floor of a cylindrical room of radius r returns to the point of projection after three elastic collisions with the walls and the ceiling. If the particle remains in air for time T, find the speed of projection.

Important Questions on Kinematics

Learn and Prepare for any exam you want !

A particle projected at an angle $θ$ with the horizontal from the centre of the floor of a cylindrical room of radius $r$ returns to the point of projection after three elastic collisions with the walls and the ceiling. If the particle remains in air for time $T$ , find the speed of projection.