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Find the time after which the particle's initial velocity will be perpendicular to instantaneous velocity when it is projected with $30 m / s$ from horizontal ground by making an angle $60 °$ with vertical.

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Important Questions on Motion in a Plane

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

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?

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).

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

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 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?

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 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

MEDIUM

Physics>Mechanics>Motion in a Plane>Projectile Motion

A ball is thrown horizontally from a height with a certain initial velocity at time

t = 0

. The ball bounces repeatedly from the ground with the coefficient of restitution less than

1

as shown.

Neglect air resistance and taking the upward direction as positive, which figure qualitatively depicts the vertical component of the ball's velocity

(v_{y})

as a function of time

(t)

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

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 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

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

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

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

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

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

A person walks

25 °

north of east for

3.18 km

. How far would she have to walk due north and then due east to arrive at the same location?

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 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:

Find the time after which the particle's initial velocity will be perpendicular to instantaneous velocity when it is projected with 30 m/s from horizontal ground by making an angle 60° with vertical.

Important Questions on Motion in a Plane

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Find the time after which the particle's initial velocity will be perpendicular to instantaneous velocity when it is projected with $30 m / s$ from horizontal ground by making an angle $60 °$ with vertical.