Motion in a Plane Set-1

Question 1

An object is thrown vertically upwards. At its maximum height, which of the following quantity becomes zero?

Accepted Answer

Momentum

Answer

Potential energy

Answer

Acceleration

Answer

Force

Question 2

A ball is projected vertically upward with an initial velocity of $50  	ext{ms}^{-1}$ at $t = 0s$. At $t = 2s$, another ball is projected vertically upward with same velocity. At $t =$ ______ s, second ball will meet the first ball ($g = 10  	ext{ms}^{-2}$)

Question 3

A body is projected from the ground at an angle of $45^\circ$ with the horizontal. Its velocity after $2s$ is $20  	ext{ms}^{-1}$. The maximum height reached by the body during its motion is ______ m. (use $g = 10  	ext{ms}^{-2}$)

Question 4

A fighter jet is flying horizontally at a certain altitude with a speed of $200  	ext{ms}^{-1}$. When it passes directly overhead an anti-aircraft gun, a bullet is fired from the gun, at an angle $	heta$ with the horizontal, to hit the jet. If the bullet speed is $400  	ext{m/s}$, the value of $	heta$ will be…….

Question 5

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

Accepted Answer

$	an\alpha - 5 \sec \alpha$

Answer

$	an\alpha + 5 \sec \alpha$

Answer

$2 	an\alpha - 5 \sec \alpha$

Answer

$2 	an\alpha + 5 \sec \alpha$

Question 6

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 $15\sqrt{2}  	ext{km/h}$, the rain drops hit her head vertically. The speed of rain drops with respect to the moving girl is :

Accepted Answer

$10\sqrt{2}  	ext{km/h}$

Answer

$5\sqrt{3}  	ext{km/h}$

Answer

$10\sqrt{3}  	ext{km/h}$

Answer

$20  	ext{km/h}$

Question 7

Motion of particle in $x$–$y$ plane is described by a set of following equations $x = 4 \sin \left( \frac{\pi}{2} - \omega t ight)  	ext{m}$ and $y = 4 \sin (\omega t)  	ext{m}$. The path of particle will be

Accepted Answer

Circular

Answer

Helical

Answer

Parabolic

Answer

Elliptical

Question 8

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

Accepted Answer

$50  m$

Answer

$25  m$

Answer

$100  m$

Answer

$200  m$

Question 9

A particle is moving in a straight line such that its velocity is increasing at $5  	ext{ms}^{-1}$ per meter. The acceleration of the particle is ______ $	ext{ms}^{-2}$ at a point where its velocity is $20  	ext{ms}^{-1}$.

Question 10

Two projectiles are thrown with same initial velocity making an angle of $45^\circ$ and $30^\circ$ with the horizontal respectively. The ratio of their range respectively will be

Accepted Answer

$2 : \sqrt{3}$

Answer

$1 : \sqrt{2}$

Answer

$\sqrt{2} : 1$

Answer

$\sqrt{3} : 2$

Question 11

A ball is thrown vertically upwards with a velocity of $19.6  	ext{ms}^{-1}$ from the top of a tower. The ball strikes the ground after $6  s$. The height from the ground up to which the ball can rise will be $\left(\frac{k}{5}ight)  m$. The value of $k$ is ______ (use $g = 9.8  	ext{m/s}^{-2}$)

Question 12

A ball is projected from the ground with a speed $15	ext{ms}^{-1}$ at an angle $	heta$ with horizontal so that its range and maximum height are equal, then ‘$	an 	heta$’ will be equal to

Accepted Answer

$4$

Answer

$1/4$

Answer

$1$

Answer

$2$

Question 13

Two projectiles thrown at $30^\circ$ and $45^\circ$ with the horizontal respectively, reach the maximum height in same time. The ratio of their initial velocities is

Accepted Answer

$\sqrt{2} : 1$

Answer

$1 : \sqrt{2}$

Answer

$2 : 1$

Answer

$1 : 2$

Question 14

If the initial velocity in horizontal direction of a projectile is unit vector $\hat{i}$ and the equation of trajectory is $y = 5x(1 - x)$. The $y$ component vector of the initial velocity is ______ $\hat{j}$. (Take $g = 10	ext{m/s}^2$)

Question 15

A body of mass $10  kg$ is projected at an angle of $45^\circ$ with the horizontal. The trajectory of the body is observed to pass through a point $(20, 10)$. If $T$ is the time of flight, then the momentum vector, at time $t = \frac{T}{\sqrt{2}}$, is ______ (Take $g = 10  	ext{m/s}^2$)

Accepted Answer

$100\sqrt{2}\hat{i} + (100\sqrt{2} - 200)\hat{j}$

Answer

$100\hat{i} + (100\sqrt{2} - 200)\hat{j}$

Answer

$100\sqrt{2}\hat{i} + (100 - 200\sqrt{2})\hat{j}$

Answer

$100\hat{i} + (100 - 200\sqrt{2})\hat{j}$

Question 16

A ball is projected with kinetic energy $E$, at an angle of $60^\circ$ to the horizontal. The kinetic energy of this ball at the highest point of its flight will become:

Accepted Answer

$E/4$

Answer

Zero

Answer

$E/2$

Answer

$E$

Question 17

An object is projected in the air with initial velocity $u$ at an angle $	heta$. 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 first object. The initial velocity of the angle of projection, at which the second object is projected, will be ______ degree. (Mark the smallest angle possible)

Question 18

A person is swimming with a speed of $10  	ext{m/s}$ at an angle of $120^\circ$ with the flow and reaches to a point directly opposite on the other side of the river. The speed of the flow is ‘$x$’ m/s. The value of ‘$x$’ to the nearest integer is ______.

Question 19

A force $\vec{F} = (40\hat{i} + 10\hat{j})N$ acts on a body of mass $5  kg$. If the body starts from rest, its position vector $\vec{r}$ at time $t = 10  s$, will be:

Accepted Answer

$(400\hat{i} + 100\hat{j})m$

Answer

$(100\hat{i} + 400\hat{j})m$

Answer

$(100\hat{i} + 100\hat{j})m$

Answer

$(400\hat{i} + 400\hat{j})m$

Question 20

A swimmer wants to cross a river from point A to point B. Line AB makes an angle of $30^\circ$ with the flow of river. Magnitude of velocity of the swimmer is same as that of the river. The angle $	heta$ with the line AB should be ______, so that the swimmer reaches point B.

Question 21

A bomb is dropped by fighter plane flying horizontally. To an observer sitting in the plane, the trajectory of the bomb is a:

Accepted Answer

straight line vertically down the plane

Answer

hyperbola

Answer

parabola in the direction of motion of plane

Answer

parabola in a direction opposite to the motion of plane

Question 22

If the velocity of a body related to displacement $x$ is given by $v = \sqrt{5000 + 24x}  	ext{m/s}$, then the acceleration of the body is ...... $	ext{m/s}^2$.

Question 23

A player kicks a football with an initial speed of $25  	ext{ms}^{-1}$ at an angle of $45^\circ$ from the ground. What are the maximum height and the time taken by the football to reach at the highest point during motion? (Take $g = 10  	ext{ms}^{-2}$)

Accepted Answer

$h_{	ext{max}} = 15.625  m$, $T = 1.77  s$

Answer

$h_{	ext{max}} = 10  m$, $T = 2.5  s$

Answer

$h_{	ext{max}} = 15.625  m$, $T = 3.54  s$

Answer

$h_{	ext{max}} = 3.54  m$, $T = 0.125  s$

Question 24

A helicopter is flying horizontally with a speed '$v$' at an altitude '$h$' has to drop a food packet for a man on the ground. What is the distance of helicopter from the man when the food packet is dropped?

Accepted Answer

$\sqrt{\frac{2v^2h}{g} + h^2}$

Answer

$\sqrt{\frac{2gh}{v^2} + 1} \cdot h$

Answer

$\sqrt{\frac{2gh}{v^2} + h^2}$

Answer

$\sqrt{\frac{2gh}{v^2} + h}$

Question 25

A particle is moving with constant acceleration '$a$'. Following graph shows $v^2$ versus $x$ (displacement) plot. The acceleration of the particle is___$	ext{m/s}^2$.

Question 26

Starting from the origin at time $t = 0$, with initial velocity $5\hat{j}  	ext{ms}^{-1}$, a particle moves in the $x$–$y$ plane with a constant acceleration of $(10\hat{i} + 4\hat{j})  	ext{ms}^{-2}$. At time $t$, its coordinates are $(20  m, y_0  m)$. The values of $t$ and $y_0$, are respectively:

Accepted Answer

$2s$ and $18  m$

Answer

$4s$ and $52  m$

Answer

$2s$ and $24  m$

Answer

$5s$ and $25  m$

Question 27

A Tennis ball is released from a height $h$ and after freely falling on a wooden floor it rebounds and reaches height $\frac{h}{2}$. The velocity versus height of the ball during its motion may be represented graphically by:

Accepted Answer

Graph C

Answer

Graph A

Answer

Graph B

Answer

Graph D

Question 28

When a car is at rest, its driver sees rain drops falling on it vertically. When driving the car with speed $v$, he sees that rain drops are coming at an angle $60^\circ$ from the horizontal. On further increasing the speed of the car to $(1 + \beta)v$, this angle changes to $45^\circ$. The value of $\beta$ is close to:

Accepted Answer

$0.73$

Answer

$0.41$

Answer

$0.50$

Answer

$0.37$

Question 29

A particle starts from the origin at $t = 0$ with an initial velocity of $3.0\hat{i}  	ext{m/s}$ and moves in the $x$–$y$ plane with a constant acceleration $(6.0\hat{i} + 4.0\hat{j})  	ext{m/s}^2$. The $x$-coordinate of the particle at the instant when its $y$-coordinate is $32  m$ is $D$ meters. The value of $D$ is:

Accepted Answer

$60$

Answer

$32$

Answer

$50$

Answer

$40$

Question 30

A particle moves such that its position vector $\vec{r}(t) = \cos \omega t \hat{i} + \sin \omega t \hat{j}$ where $\omega$ is a constant and $t$ is time. Then which of the following statements is true for the velocity $\vec{v}(t)$ and acceleration $\vec{a}(t)$ of the particle:

Accepted Answer

$\vec{v}$ is perpendicular to $\vec{r}$ and $\vec{a}$ is directed towards the origin

Answer

$\vec{v}$ is perpendicular to $\vec{r}$ and $\vec{a}$ is directed away from the origin

Answer

$\vec{v}$ and $\vec{a}$ both are perpendicular to $\vec{r}$

Answer

$\vec{v}$ and $\vec{a}$ both are parallel to $\vec{r}$

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