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An object $A$ is kept fixed at the point $x = 3 m$ and $y = 1.25 m$ on a plank $P$ raised above the ground. At time $t = 0$ the plank starts moving along the $+ x$ direction with an acceleration $1.5 m s^{- 2} .$ At the same instant a stone is projected from the origin with a velocity $u$ as shown. A stationary person on the ground observes the stone hitting the object during its downward motion at an angle of $45 °$ to the horizontal. All the motions are in the $x - y$ plane. Find $u$ and the time after which the stone hits the object. Take $g = 10 m s^{- 2} .$

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Important Questions on Motion in a Plane

MEDIUM

Physics>Mechanics>Motion in a Plane>Projectile Motion

A projectile is fired from the surface of the earth with a velocity of

5 m s^{- 1}

and angle

θ

with the horizontal. Another projectile fired from another planet with a velocity of

3 {m s}^{- 1}

at the same angle follows a trajectory which is identical with the trajectory of the projectile fired from the earth. The value of the acceleration due to gravity on the planet is: (given

= 9.8 m s^{- 2}

)

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}

)

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______

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:

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 _____________.

MEDIUM

Physics>Mechanics>Motion in a Plane>Projectile Motion

Two particles are projected from the same point with the same speed u such that they have the same range R, but different maximum heights,

h_{1}

and

h_{2} .

Which of the following is correct?

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).

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

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 :

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

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

MEDIUM

Physics>Mechanics>Motion in a Plane>Projectile Motion

A ball is thrown horizontally from a height of

100 m

with an initial speed of

15 m / s

. How far does it travel horizontally in the first

2

seconds?

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?

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}

)

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

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 _____.

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}]

HARD

Physics>Mechanics>Motion in a Plane>Projectile Motion

A small boy is throwing a ball towards a wall

6 m

in front of him. He releases the ball at a height of

1.4 m

from the ground. The ball bounces from the wall at a height of

3 m

, rebounds from the ground and reaches the boy's hand exactly at the point of release. Assuming the two bounces (one from the wall and the other from the ground) to be perfectly elastic, how far ahead of the boy did the ball bounce from the ground?

EASY

Physics>Mechanics>Motion in a Plane>Projectile Motion

Two guns

A

and

B

can fire bullets at speeds

1 km s^{- 1}

and

2 km s^{- 1}

respectively. From a point on a horizontal ground, they are fired in all possible directions. The ratio of maximum areas covered by the bullets fired by the two guns, on the ground is:

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

Important Questions on Motion in a Plane

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