EASY

Earn 100

A fighter plane is flying horizontally at an altitude of 1.5 km with speed 720 km/h. At what angle of sight (w.r.t. horizontal) when the target is seen, should the pilot drop the bomb in order to attack the target ?

(Answer in degrees correct to two decimal places)

50% studentsanswered this correctly

Important Questions on Motion in a Plane

MEDIUM

Physics>Mechanics>Motion in a Plane>Motion in a Plane with Constant Acceleration

Two forces

P

and

Q

, of magnitude

2 F

and

3 F

, respectively, are at an angle

θ

with each other. If the force

Q

is doubled, then their resultant also gets doubled. Then, the angle

θ

is:

MEDIUM

Physics>Mechanics>Motion in a Plane>Motion in a Plane with Constant Acceleration

A particle is moving with a velocity

\vec{v} = K (y \hat{i} + x \hat{j}),

where

K

is a constant.

The general equation for its path is:

MEDIUM

Physics>Mechanics>Motion in a Plane>Motion in a Plane with Constant Acceleration

Two vectors

\vec{A}

and

\vec{B}

have equal magnitudes. The magnitude of

(\vec{A} + \vec{B})

n

times the magnitude of

(\vec{A} - \vec{B})

. The angle between

\vec{A}

and

\vec{B}

is:

EASY

Physics>Mechanics>Motion in a Plane>Motion in a Plane with Constant Acceleration

Force

\vec{F}

applied on a body is written as

\vec{F} = (\hat{n} \times \vec{F}) \cdot \hat{n} + \vec{G}

, where

\hat{n}

is a unit vector. The vector

\vec{G}

is equal to

EASY

Physics>Mechanics>Motion in a Plane>Motion in a Plane with Constant Acceleration

A particle moves according to the equation

x = a \sin ω t

and

y = a (1 - \cos ω t)

. The path of the particle is

MEDIUM

Physics>Mechanics>Motion in a Plane>Motion in a Plane with Constant Acceleration

A vector

\vec{A}

is rotated by a small angle

∆ θ

radians

(∆ θ ≪ 1)

to get a new vector

\vec{B}

. In that case

|\vec{B} - \vec{A}|

is :

EASY

Physics>Mechanics>Motion in a Plane>Motion in a Plane with Constant Acceleration

If the magnitude of sum of two vectors is equal to the magnitude of difference of the two vectors, the angle between these vectors is:

MEDIUM

Physics>Mechanics>Motion in a Plane>Motion in a Plane with Constant Acceleration

The sum of two forces

\vec{P}

and

\vec{Q}

\vec{R}

such that

|\vec{R}| = |\vec{P}|

. The angle

θ

(in degree) that the resultant of

2 \vec{P}

and

\vec{Q}

will make with

\vec{Q}

is, ________

EASY

Physics>Mechanics>Motion in a Plane>Motion in a Plane with Constant Acceleration

A body of mass $2 kg$ moves under a force of $(2 \hat{i} + 3 \hat{j} + 5 \hat{k}) N$ It starts from rest and was at the origin initially. After $4 s$ , its new coordinates are $(8, b, 20)$ . The value of $b$ is ______.

(Round off to the Nearest Integer)

MEDIUM

Physics>Mechanics>Motion in a Plane>Motion in a Plane with Constant Acceleration

The position of a particle as a function of time is given by

\vec{r} (t) = A \cos ω t \hat{i} + B \sin ω t \hat{j}

where

A

and

B

are two real positive constants with

A > B

. The orbit of the particle looks like-

EASY

Physics>Mechanics>Motion in a Plane>Motion in a Plane with Constant Acceleration

Let

\vec{A} = (\hat{i} + \hat{j}) a n d \vec{B} = (2 \hat{i} - \hat{j})

. The magnitude of a coplanar vector

\vec{C}

such that

\vec{A} . \vec{C} = \vec{B} . \vec{C} = \vec{A} . \vec{B}

is given by:

MEDIUM

Physics>Mechanics>Motion in a Plane>Motion in a Plane with Constant Acceleration

The trajectory of a projectile projected from origin is given by the equation

y = x - \frac{2 x^{2}}{5} .

The initial velocity of the projectile is

MEDIUM

Physics>Mechanics>Motion in a Plane>Motion in a Plane with Constant Acceleration

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>Motion in a Plane with Constant Acceleration

If vectors

\vec{A} = \cos ω t \hat{i} + s i n ω t \hat{j}

and

\vec{B} = c o s \frac{ω t}{2} \hat{i} + \sin \frac{ω t}{2} \hat{j}

are functions of time, then the value of

t

at which they are orthogonal to each other is:

EASY

Physics>Mechanics>Motion in a Plane>Motion in a Plane with Constant Acceleration

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?

MEDIUM

Physics>Mechanics>Motion in a Plane>Motion in a Plane with Constant Acceleration

A particle starts from the origin at

t = 0

with an initial velocity of

(3.0 \hat{i}) m s^{- 1}

and moves in the

x - y

plane with a constant acceleration

(6.0 \hat{i} + 4.0 \hat{j}) m s^{- 2}

. The

x -

coordinate of the particle at the instant when its

y -

coordinate is

32 m

D

meters. The value of

D

is:

MEDIUM

Physics>Mechanics>Motion in a Plane>Motion in a Plane with Constant Acceleration

Let

|\vec{A_{1}}| = 3, |\vec{A_{2}}| = 5

and

|\vec{A_{1}} + \vec{A_{2}}| = 5 .

The value of

(2 \vec{A_{1}} + 3 \vec{A_{2}}) \cdot (3 \vec{A_{1}} - 2 \vec{A_{2}})

is:

HARD

Physics>Mechanics>Motion in a Plane>Motion in a Plane with Constant Acceleration

Two paper screens A and B are separated by

150 m

. A bullet pierces A and then B. The hole in B is

15 cm

below the hole in A. If the bullet is traveling horizontally at the time of hitting A, then the velocity of the bullet at A is:

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

HARD

Physics>Mechanics>Motion in a Plane>Motion in a Plane with Constant Acceleration

Consider a particle moving in the xy plane with velocity

\vec{v} = a \hat{i} + b x \hat{j},

where

\hat{i}

and

\hat{j}

are the unit vectors along

x

and

y

axes and

a^{'}

and

b^{'}

are constants. If the initial position of the particle is

x = y = 0,

the equation to describe the particle's trajectory in the plane is

EASY

Physics>Mechanics>Motion in a Plane>Motion in a Plane with Constant Acceleration

The trajectory of a projectile near the surface of the earth is given as

y = 2 x - 9 x^{2} .

If it were launched at an angle

θ_{0}

with speed

v_{0}

then

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

A fighter plane is flying horizontally at an altitude of 1.5 km with speed 720 km/h. At what angle of sight (w.r.t. horizontal) when the target is seen, should the pilot drop the bomb in order to attack the target ? (Answer in degrees correct to two decimal places)

Important Questions on Motion in a Plane

Learn and Prepare for any exam you want !

A fighter plane is flying horizontally at an altitude of 1.5 km with speed 720 km/h. At what angle of sight (w.r.t. horizontal) when the target is seen, should the pilot drop the bomb in order to attack the target ?

(Answer in degrees correct to two decimal places)