Motion in a Plane PYQs - Last 10 Years

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Practice 84 JEE Main Physics questions from Motion in a Plane. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.

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Last 10 Years Motion in a Plane Questions

Showing 50 of 84 filtered questions.

1Motion In A Plane

Two identical bodies, projected with the same speed at two different angles cover the same horizontal range $R$. If the time of flight of these bodies are 5 s and 10 s , respectively, then the value of $R$ is
$\_\_\_\_$ m. (Take $g=10 \mat...

2Motion In A Plane

The two projectiles are projected with the same initial velocities at the $15^{\circ}$ and $30^{\circ}$ with respect to the horizontal. The ratio of their ranges is $1: x$. The value of $x$ is

3Motion In A Plane

A gun mounted on the ground fires bullets in all directions with same speed. The farthest distance the bullets could reach is 6.4 m . The speed of the bullets from the gun is $\_\_\_\_$ $\mathrm{m} / \mathrm{s}$.
$$ \text { (take } \mathrm{...

INTEGER+4 / -12026

4Motion In A Plane

If $x$ and $y$ coordinates of a projectile as a function of time $(t)$ are given as $24 t$ and $43.6 t-4.9 t^2$, respectively, then the angle (in degrees) made by the projectile with horizontal when $t=2 \mathrm{~s}$ is $\_\_\_\_$ .

5Motion In A Plane

At $t=0$, a body of mass 100 g starts moving under the influence of a force $(5 \hat{\mathrm{i}}+10 \hat{\mathrm{j}}) \mathrm{N} \cdot$ After 2 s its position is $(2 x \hat{\mathrm{i}}+5 y \hat{\mathrm{j}}) \mathrm{m}$. The ratio $x: y$ is ...

6Motion In A Plane

A boy throws a ball into air at $45^{\circ}$ from the horizontal to land it on a roof of a building of height $H$. If the ball attains maximum height in 2 s and lands on the building in 3 s after launch, then value of $H$ is $\_\_\_\_$ m.
$...

7Motion In A Plane

A projectile is thrown upward at an angle $60^{\circ}$ with the horizontal. The speed of the projectile is $20 \mathrm{~m} / \mathrm{s}$ when its direction of motion is $45^{\circ}$ with the horizontal. The initial speed of the projectile i...

8Motion In A Plane

A river of width 200 m is flowing from west to east with a speed of 18 km/h. A boat, moving with speed of 36 km/h in still water, is made to travel one-round trip (bank to bank of the river). Minimum time taken by the boat for this journey ...

9Motion In A Plane

Two balls with same mass and initial velocity, are projected at different angles in such a way that maximum height reached by first ball is 8 times higher than that of the second ball. $T_1$ and $T_2$ are the total flying times of first and...

10Motion In A Plane

Two projectiles are fired from ground with same initial speeds from same point at angles $\left(45^{\circ}+\right.$ $\alpha)$ and $\left(45^{\circ}-\alpha\right)$ with horizontal direction. The ratio of their times of flights is

11Motion In A Plane

A helicopter flying horizontally with a speed of 360 km/h at an altitude of 2 km, drops an object at an instant. The object hits the ground at a point O, 20 s after it is dropped. Displacement of 'O' from the position of helicopter where th...

12Motion In A Plane

The angle of projection of a particle is measured from the vertical axis as $\phi$ and the maximum height reached by the particle is $\mathrm{h}_{\mathrm{m}}$. Here $\mathrm{h}_{\mathrm{m}}$ as function of $\phi$ can be presented as

13Motion In A Plane

A particle is projected with velocity $u$ so that its horizontal range is three times the maximum height attained by it. The horizontal range of the projectile is given as $\frac{n u^2}{25 g}$, where value of $n$ is: (Given, ' $g$ ' is the ...

14Motion In A Plane

A river is flowing from west to east direction with speed of $9 \mathrm{~km} \mathrm{~h}^{-1}$. If a boat capable of moving at a maximum speed of $27 \mathrm{~km} \mathrm{~h}^{-1}$ in still water, crosses the river in half a minute, while m...

15Motion In A Plane

The maximum speed of a boat in still water is 27 km/h. Now this boat is moving downstream in a river flowing at 9 km/h. A man in the boat throws a ball vertically upwards with speed of 10 m/s. Range of the ball as observed by an observer at...

INTEGER+4 / -12025

16Motion In A Plane

Two projectiles are fired with same initial speed from same point on ground at angles of $(45^\circ - \alpha)$ and $(45^\circ + \alpha)$, respectively, with the horizontal direction. The ratio of their maximum heights attained is :

17Motion In A Plane

An object of mass ' m ' is projected from origin in a vertical xy plane at an angle $45^{\circ}$ with the $\mathrm{x}-$ axis with an initial velocity $\mathrm{v}_0$. The magnitude and direction of the angular momentum of the object with res...

18Motion In A Plane

The position vector of a moving body at any instant of time is given as $\overrightarrow{\mathrm{r}}=\left(5 \mathrm{t}^2 \hat{i}-5 \mathrm{t} \hat{j}\right) \mathrm{m}$. The magnitude and direction of velocity at $t=2 s$ is,

19Motion In A Plane

A particle is projected at an angle of $30^{\circ}$ from horizontal at a speed of $60 \mathrm{~m} / \mathrm{s}$. The height traversed by the particle in the first second is $\mathrm{h}_0$ and height traversed in the last second, before it r...

INTEGER+4 / -12025

20Motion In A Plane

A ball of mass 100 g is projected with velocity $20 \mathrm{~m} / \mathrm{s}$ at $60^{\circ}$ with horizontal. The decrease in kinetic energy of the ball during the motion from point of projection to highest point is

21Motion In A Plane

A body of mass M thrown horizontally with velocity v from the top of the tower of height H touches the ground at a distance of \(100 \mathrm{~m}\) from the foot of the tower. A body of mass \(2 \mathrm{~M}\) thrown at a velocity $$\frac{v}{...

INTEGER+4 / -12024

22Motion In A Plane

The angle of projection for a projectile to have same horizontal range and maximum height is :

23Motion In A Plane

The maximum height reached by a projectile is \(64 \mathrm{~m}\). If the initial velocity is halved, the new maximum height of the projectile is ______ \(\mathrm{m}\).

INTEGER+4 / -12024

24Motion In A Plane

The co-ordinates of a particle moving in \(x\)-\(y\) plane are given by : \(x=2+4 \mathrm{t}, y=3 \mathrm{t}+8 \mathrm{t}^2\).
The motion of the particle is :

25Motion In A Plane

Projectiles A and B are thrown at angles of \(45^{\circ}\) and \(60^{\circ}\) with vertical respectively from top of a \(400 \mathrm{~m}\) high tower. If their ranges and times of flight are same, the ratio of their speeds of projection $$v...

26Motion In A Plane

A ball rolls off the top of a stairway with horizontal velocity \(u\). The steps are \(0.1 \mathrm{~m}\) high and \(0.1 \mathrm{~m}\) wide. The minimum velocity \(u\) with which that ball just hits the step 5 of the stairway will be $$\sqrt...

INTEGER+4 / -12024

27Motion In A Plane

A particle starts from origin at \(t=0\) with a velocity \(5 \hat{i} \mathrm{~m} / \mathrm{s}\) and moves in \(x-y\) plane under action of a force which produces a constant acceleration of \((3 \hat{i}+2 \hat{j}) \mathrm{m} / \mathrm{s}^2\)...

INTEGER+4 / -12024

28Motion In A Plane

Position of an ant (\(\mathrm{S}\) in metres) moving in \(\mathrm{Y}\)-\(\mathrm{Z}\) plane is given by \(S=2 t^2 \hat{j}+5 \hat{k}\) (where \(t\) is in second). The magnitude and direction of velocity of the ant at $$\mathrm{t}=1 \mathrm{~...

29Motion In A Plane

Two projectiles A and B are thrown with initial velocities of \(40 \mathrm{~m} / \mathrm{s}\) and \(60 \mathrm{~m} / \mathrm{s}\) at angles \(30^{\circ}\) and \(60^{\circ}\) with the horizontal respectively. The ratio of their ranges respec...

30Motion In A Plane

The trajectory of projectile, projected from the ground is given by \(y=x-\frac{x^{2}}{20}\). Where \(x\) and \(y\) are measured in meter. The maximum height attained by the projectile will be.

31Motion In A Plane

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R
Assertion A : When a body is projected at an angle \(45^{\circ}\), it's range is maximum.
Reason R : For maximum range, the value of $$\si...

32Motion In A Plane

The speed of a swimmer is \(4 \mathrm{~km} \mathrm{~h}^{-1}\) in still water. If the swimmer makes his strokes normal to the flow of river of width \(1 \mathrm{~km}\), he reaches a point \(750 \mathrm{~m}\) down the stream on the opposite b...

INTEGER+4 / -12023

33Motion In A Plane

The initial speed of a projectile fired from ground is \(\mathrm{u}\). At the highest point during its motion, the speed of projectile is \(\frac{\sqrt{3}}{2} u\). The time of flight of the projectile is :

34Motion In A Plane

Two bodies are projected from ground with same speeds $40 \mathrm{~ms}^{-1}$ at two different angles with respect to horizontal. The bodies were found to have same range. If one of the body was projected at an angle of $60^{\circ}$, with ho...

INTEGER+4 / -12023

35Motion In A Plane

Two objects are projected with same velocity 'u' however at different angles \(\alpha\) and \(\beta\) with the horizontal. If \(\alpha+\beta=90^\circ\), the ratio of horizontal range of the first object to the 2nd object will be :

36Motion In A Plane

The maximum vertical height to which a man can throw a ball is 136 m. The maximum horizontal distance upto which he can throw the same ball is :

37Motion In A Plane

A child stands on the edge of the cliff \(10 \mathrm{~m}\) above the ground and throws a stone horizontally with an initial speed of \(5 \mathrm{~ms}^{-1}\). Neglecting the air resistance, the speed with which the stone hits the ground will...

38Motion In A Plane

A projectile fired at \(30^{\circ}\) to the ground is observed to be at same height at time \(3 \mathrm{~s}\) and \(5 \mathrm{~s}\) after projection, during its flight. The speed of projection of the projectile is ___________ $$\mathrm{m} ~...

INTEGER+4 / -12023

39Motion In A Plane

A projectile is projected at \(30^{\circ}\) from horizontal with initial velocity \(40 \mathrm{~ms}^{-1}\). The velocity of the projectile at \(\mathrm{t}=2 \mathrm{~s}\) from the start will be : (Given \(g=10 \mathrm{~m} / \mathrm{s}^{2}\)...

40Motion In A Plane

The range of the projectile projected at an angle of 15\(^\circ\) with horizontal is 50 m. If the projectile is projected with same velocity at an angle of 45\(^\circ\) with horizontal, then its range will be

41Motion In A Plane

Two projectiles are projected at \(30^{\circ}\) and \(60^{\circ}\) with the horizontal with the same speed. The ratio of the maximum height attained by the two projectiles respectively is:

42Motion In A Plane

Two projectiles P1 and P2 thrown with speed in the ratio \(\sqrt3\) : \(\sqrt2\), attain the same height during their motion. If P2 is thrown at an angle of 60\(^\circ\) with the horizontal, the angle of projection of P1 with horizontal wil...

43Motion In A Plane

At t = 0, truck, starting from rest, moves in the positive x-direction at uniform acceleration of 5 ms\(-\)2. At t = 20 s, a ball is released from the top of the truck. The ball strikes the ground in 1 s after the release. The velocity of t...

44Motion In A Plane

A person can throw a ball upto a maximum range of 100 m. How high above the ground he can throw the same ball?

45Motion In A Plane

An object is projected in the air with initial velocity u at an angle \(\theta\). The projectile motion is such that the horizontal range R, is maximum. Another object is projected in the air with a horizontal range half of the range of fir...

INTEGER+4 / -12022

46Motion In A Plane

At time \(t=0\) a particle starts travelling from a height \(7 \hat{z} \mathrm{~cm}\) in a plane keeping z coordinate constant. At any instant of time it's position along the \(\hat{x}\) and \(\hat{y}\) directions are defined as $$3 \mathrm...

47Motion In A Plane

A girl standing on road holds her umbrella at 45\(^\circ\) with the vertical to keep the rain away. If she starts running without umbrella with a speed of 15\(\sqrt2\) kmh\(-\)1, the rain drops hit her head vertically. The speed of rain dro...

48Motion In A Plane

A projectile is launched at an angle '\(\alpha\)' with the horizontal with a velocity 20 ms\(-\)1. After 10 s, its inclination with horizontal is '\(\beta\)'. The value of tan\(\beta\) will be : (g = 10 ms\(-\)2).

49Motion In A Plane

A ball of mass m is thrown vertically upward. Another ball of mass \(2 \mathrm{~m}\) is thrown at an angle \(\theta\) with the vertical. Both the balls stay in air for the same period of time. The ratio of the heights attained by the two ba...

INTEGER+4 / -12022

50Motion In A Plane

A fighter jet is flying horizontally at a certain altitude with a speed of 200 ms\(-\)1. When it passes directly overhead an anti-aircraft gun, a bullet is fired from the gun, at an angle \(\theta\) with the horizontal, to hit the jet. If t...

INTEGER+4 / -12022