EASY

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A projectile is launched with an initial speed of $40 m s^{- 1}$ at an angle $30 °$ above the ground. The projectile lands on a hillside $2.0 s$ later. The net displacement from where the projectile was launched to where it hits the target is (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 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

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:

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 at an angle of

60 °

with the horizontal such that the vertical component of its initial velocity is

40 m s^{- 1}

. The magnitude of velocity of the projectile at one quarter of its time of flight is nearly (Acceleration due to gravity

= 10 m s^{- 2}

)

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

A particle moves in

X - Y

plane with constant acceleration

a

and is directed along the negative

Y

-axis. The equation of motion of the particle has the form

Y = p x - q x^{2},

where

p

and

q

? are positive constants. The velocity of the particle at the origin is

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

HARD

Physics>Mechanics>Motion in a Plane>Projectile Motion

In a circus, a performer throws an apple towards a hoop held at $45 m$ height by another performer standing on a high platform (see figure below). The thrower aims for the hoop and throws the apple with a speed of $24 m s^{- 1}$ . At the exact moment that the thrower released the apple, the other performer drops the hoop. The hoop falls straight down. At what height above the ground does the apple go through the hoop?

Question Image

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}

)

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

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 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 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

A stone is thrown with a velocity of

20 m s^{- 1}

at an angle

60 °

with the horizontal. The speed of the stone when its direction of motion makes

45 °

with the horizontal is

HARD

Physics>Mechanics>Motion in a Plane>Projectile Motion

Two balls are projected with the same velocity but with different angles with the horizontal. Their ranges are equal. If the angle of projection of one is

30 °

and its maximum height is

h

, then the maximum height of other will be

MEDIUM

Physics>Mechanics>Motion in a Plane>Projectile Motion

The initial velocity of a projectile is

(2 \hat{i} + 4 \hat{j}) m s^{- 1}

, where

\hat{i}

and

\hat{j}

are along horizontal and vertical directions, respectively. For

g = 10 m s^{- 2}

, the equation of the trajectory will be,

MEDIUM

Physics>Mechanics>Motion in a Plane>Projectile Motion

The trajectory of a projectile in a vertical plane is

y = α x - β x^{2},

where

α

and

β

are constants and

x & y

are respectively the horizontal and vertical distances of the projectile from the point of projection. The angle of projection

θ

and the maximum height attained

H

are respectively given by

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 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 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

A projectile is launched with an initial speed of 40 m s-1 at an angle 30° above the ground. The projectile lands on a hillside 2.0 s later. The net displacement from where the projectile was launched to where it hits the target is (Take g=10 m s-2)

Important Questions on Motion in a Plane

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A projectile is launched with an initial speed of $40 m s^{- 1}$ at an angle $30 °$ above the ground. The projectile lands on a hillside $2.0 s$ later. The net displacement from where the projectile was launched to where it hits the target is (Take $g = 10 m s^{- 2}$ )