MEDIUM

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A particle is projected with a certain velocity so as to pass through a point at a horizontal distance $R$ from the point of projection. Show that if $t_{1}$ and $t_{2}$ are the time taken to reach this point in two possible ways in which the particle can be projected with the given velocity then $t_{1} t_{2} = \frac{R}{g}$ .

Important Questions on Motion in a Plane

MEDIUM

Physics>Mechanics>Motion in a Plane>Projectile Motion

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

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

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>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

The velocity of a projectile at the initial point $A$ is $(2 \hat{i} - 3 \hat{j}) m s^{- 1}$ . Its velocity (in $m s^{- 1}$ ) at point $B$ is

Question Image

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

HARD

Physics>Mechanics>Motion in a Plane>Projectile Motion

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>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

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 mobile phone of mass

100 g

falls from the hand of a person through the window of a train. The train is accelerating at

1 m s^{- 2}

and just

20 s

have passed since it left the station from standstill. If the window is

2 m

above the ground. With what kinetic energy will the phone will hit the ground?

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

EASY

Physics>Mechanics>Motion in a Plane>Projectile Motion

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 _____.

EASY

Physics>Mechanics>Motion in a Plane>Projectile Motion

Two bodies are projected at angles

θ

and

(90^{o} - θ)

to the horizontal with the same speed. The ratio of their times of flight is

HARD

Physics>Mechanics>Motion in a Plane>Projectile Motion

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

HARD

Physics>Mechanics>Motion in a Plane>Projectile Motion

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>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}

)

HARD

Physics>Mechanics>Motion in a Plane>Projectile Motion

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

HARD

Physics>Mechanics>Motion in a Plane>Projectile Motion

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

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

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

HARD

Physics>Mechanics>Motion in a Plane>Projectile Motion

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 is projected with a certain velocity so as to pass through a point at a horizontal distance R from the point of projection. Show that if t1 and t2 are the time taken to reach this point in two possible ways in which the particle can be projected with the given velocity then t1t2=Rg.

Important Questions on Motion in a Plane

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