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Master Resource Book in JEE Main Physics

D. B. Singh

Chapter 4

Projectile Motion - all with Video Answers

Educators

Section 1

Round 1

02:07

Problem 1

The horizontal range of a projectile fired at an angle of $15^{\circ}$ is $50 \mathrm{~m}$. If it is fired with the same speed at an angle of $45^{\circ}$, its range will be
(a) $60 \mathrm{~m}$
(b) $\underline{71} \bar{m}$
(c) $100 \mathrm{~m}$
(d) $141 \mathrm{~m}$

Vishal Gupta
Vishal Gupta
Numerade Educator
01:20

Problem 2

A tennis ball rolls off the top of a sister case way with
a horizontal velocity $u \mathrm{~ms}^{-1}$. If the steps are $b$ metre wide and $h$ meter high, the ball will hit the edge of the $n$th step, if
(al $n=\frac{2 h u}{g b^{2}}$
(b) $n=\frac{2 h u^{2}}{g b^{2}}$
(c) $n=\frac{2 h u^{2}}{g b}$
(d) $n=\frac{h u^{2}}{g b^{2}}$

Varsha Aggarwal
Varsha Aggarwal
Numerade Educator
02:24

Problem 3

A bomber plane moves horizontally with a speed of $500 \mathrm{~ms}^{-1}$ and a bomb releases from it, strikes the ground in 10 s. Angle at which it strikes the ground will be $\left(g=10 \mathrm{~ms}^{-2}\right)$
(a) $\tan ^{-1}\left(\frac{1}{5}\right)$
(b) $\tan \left(\frac{1}{5}\right)$
(c) $\tan ^{-1}(1)$
(d) $\tan ^{-1}(5)$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
01:06

Problem 4

An aeroplane is flying in a horizontal direction with a velocity $600 \mathrm{kmh}^{-1}$ at a height of $1960 \mathrm{~m}$. When it is vertically above the point $A$ on the ground, a body is dropped from it. The body strikes the ground at point $B$. Calculate the distance $A B$.
(a) $3.33 \mathrm{~km}$
(b) $333 \mathrm{~km}$
(c) $33.3 \mathrm{~km}$
(d) $3330 \mathrm{~km}$

Narayan Hari
Narayan Hari
Numerade Educator
05:44

Problem 5

The height $y$ and distancex along the horizontal for a body projected in the xy-plane are given by $y=8 t-5 t^{2}$ and $x=6 t .$ The initial speed of projection is
(a) $8 \mathrm{~m} / \mathrm{s}$
(b) $9 \mathrm{~m} / \mathrm{s}$
(c) $10 \mathrm{~m} / \mathrm{s}$
(d) $(10 / 3) \mathrm{m} / \mathrm{s}$

Nadia Parveen
Nadia Parveen
Numerade Educator
02:38

Problem 6

Water is flowing from a horizontal pipe fixed at a height of $2 \mathrm{~m}$ from the ground. If it falls at a horizontal distance of $3 \mathrm{~m}$, as shown in figure, the speed of water when it leaves the pipe is (Take, $g=9.8 \mathrm{~ms}^{-2}$ )
(a) $2.4 \mathrm{~ms}^{-1}$
(b) $4.7 \mathrm{~ms}^{-1}$
(c) $7.4 \mathrm{~ms}^{-1}$
(d) $6.2 \mathrm{~ms}^{-1}$

Nathan Silvano
Nathan Silvano
Numerade Educator
01:35

Problem 7

A stone is just released from the window of a moving train along a horizontal straight track. The stone will hit the ground following
(a) straight path
(b) circular path
(c) parabolic path
(d) hyperbolic path

Satpal Satpal
Satpal Satpal
Numerade Educator
01:05

Problem 8

A man standing on a hill top projects a stone horizontally with speed $v_{0}$ as shown in figure. Taking the coordinate system as given in the figure. The coordinates of the point where the stone will hit the hill surface
(a) $\left(\frac{2 v_{0}^{2} \tan \theta}{g}, \frac{-2 v_{0}^{2} \tan ^{2} \theta}{g}\right)$
(b) $\left(\frac{2 v_{2}^{2}}{g}, \frac{2 v_{0}^{2} \tan ^{2} \theta}{g}\right)$
(c) $\left(\frac{2 V_{0}^{2} \tan \theta}{g}, \frac{2 v_{0}^{2}}{g}\right)$
(d) $\left(\frac{2 v_{0}^{2} \tan ^{7} \theta}{g}, \frac{2 v_{0}^{2} \tan \theta}{g}\right)$

Hast Aggarwal
Hast Aggarwal
Numerade Educator
06:38

Problem 9

A particle moves in the $x y$-plane with velocity $v_{x}=8 t-2$ and $v_{y}=2$ If it passes through the point $x=14$ and $y=4$ at $t=2$ s, find the equation $(x-y$ relation) of the path.
(a) $x=y^{2}-y+2$
(b) $x=2 y^{2}+2 y-3$
(c) $x=3 y^{2}+5$
(d) Cannot be found from above data

Nadia Parveen
Nadia Parveen
Numerade Educator
03:10

Problem 10

The ceiling of a long hall is $25 \mathrm{~m}$ high. Then, the maximum horizontal distance that a ball thrown with a speed of $40 \mathrm{~m} / \mathrm{s}$ can go without hitting the ceiling of the hall, is [NCERT Exemplar]
(a) $95.5 \mathrm{~m}$
(b) $105.5 \mathrm{~m}$
(c) $100 \mathrm{~m}$
(d) $150.5 \mathrm{~m}$

Vishal Gupta
Vishal Gupta
Numerade Educator
03:13

Problem 11

A particle leaves the origin with an initial velocity $\mathbf{v}=(3.00 \hat{\mathrm{i}}) \mathrm{ms}^{-1}$ and a constant acoeleration
$\mathbf{a}=(-1.00 \hat{\mathrm{i}}-0.50 \hat{\mathrm{j}}) \mathrm{ms}^{-2}$. When the particle reaches
its maximum $x$-coordinate, what is its $y$-component a velocity?
(a) $-2.0 \mathrm{~ms}^{-1}$
(b) $-1.0 \mathrm{~ms}^{-1}$
(c) $-1.5 \mathrm{~ms}^{-1}$
(d) $1.0 \mathrm{~ms}^{-1}$

Averell Hause
Averell Hause
Carnegie Mellon University
04:23

Problem 12

A projectile can have same range from two angles of projection with same initial speed. If $h_{1}$ and $h_{2}$ be the maximum heights, then
(a) $R=\sqrt{h h}$
(b) $R=\sqrt{2 h / h}$
(c) $R=2 \sqrt{h_{1} h_{2}}$
(d) $R=4 \sqrt{h_{h}}$

Vysakh M
Vysakh M
Numerade Educator
01:05

Problem 13

A stone is thrown at an angle $\theta$ to be the horizontal reaches a maximum height $H$. Then, the time of flight of stone will be
(a) $\sqrt{\frac{2 H}{g}}$
(b) $2 \sqrt{\frac{2 H}{g}}$
(c) $\frac{2 \sqrt{2 H \sin \theta}}{g}$
(d) $\frac{\sqrt{2 H \sin \theta}}{g}$

Hast Aggarwal
Hast Aggarwal
Numerade Educator
01:25

Problem 14

A bomb is dropped on an enemy post by an aeroplane flying horizontally with a velocity of $60 \mathrm{kmh}^{-1}$ and at
a height of $490 \mathrm{~m}$. At the time of dropping the bomb, how far the aeroplane should be from the enemy post so that the bomb may directly hit the target?
(a) $\frac{400}{3} \mathrm{~m}$
(b) $\frac{500}{3} \mathrm{~m}$
(c) $\frac{1700}{3} \mathrm{~m}$
(d) $498 \mathrm{~m}$

Varsha Aggarwal
Varsha Aggarwal
Numerade Educator
01:02

Problem 15

A body projected with velocity $u$ at projection angle $\theta$ has horizontal range $R$. For the same velocity and projection angle, its range on the moon surface will be $g_{\text {moen }}=g_{\text {earth }} / 6$ )
(a) $36 R$
(b) $\frac{R}{36}$
(c) $\frac{R}{16}$
(d) $6 R$

Varsha Aggarwal
Varsha Aggarwal
Numerade Educator
05:26

Problem 16

A boy throws a ball with a velocity $u$ at an angle $\theta$ with the horizontal. At the same instant he starts running with uniform velocity to eatch the ball before if hits the ground. To achieve this he should run with a velocity of
(a) $u \cos \theta$
(b) $u \sin \theta$
(c) $u \tan \theta$
(d) $u \sec \theta$

Sheh Lit Chang
Sheh Lit Chang
University of Washington
02:02

Problem 17

An arrow is shot into air. Its range is $200 \mathrm{~m}$ and its time of flight is $5 \mathrm{~s}$. If $=10 \mathrm{~m} / \mathrm{s}^{2}$, then horizontal component of velocity and the maximum height will be respectively
(a) $20 \mathrm{~m} / \mathrm{s}, 62.50 \mathrm{~m}$
(b] $40 \mathrm{~m} / \mathrm{s}, 31.25 \mathrm{~m}$
(c) $80 \mathrm{~m} / \mathrm{s}, 62.5 \mathrm{~m}$
(d) None of these

Sanu Kumar
Sanu Kumar
Numerade Educator
02:44

Problem 18

A body of mass $m$ thrown horizontally with velocity $v$, from the top of tower of height $h$ touches the level ground at distance of $250 \mathrm{~m}$ from the foot of the tower. A body of mass $2 \mathrm{~m}$ thrown horizontally with velocity $\frac{v}{2}$, from the top of tower of height $4 h$ will touch the level ground at a distance $x$ from the foot of tower. The value of $x$ is
(a) $250 \mathrm{~m}$
(b) $500 \mathrm{~m}$
(c) $125 \mathrm{~m}$
(d) $250 \sqrt{2} \mathrm{~m}$

Vysakh M
Vysakh M
Numerade Educator
01:01

Problem 19

A ball is thrown up with a certain velocity at an angle
$\theta$ to the horizontal. The kinetic energy (KE) of the ball varies in the horizontal displacement xas
[a]
(b)
(c)
(d)

Narayan Hari
Narayan Hari
Numerade Educator
03:07

Problem 20

Two paper sereen $A$ and $B$ are separated by a distance of $100 \mathrm{~m}$. A bullet pierces $A$ and $B$. The hole in $B$ is $10 \mathrm{~cm}$ below the hole in $A$. If the bullet is travelling horizontally at the time of hitting $A$. Then, the velocity of the bullet at $A$ is
(a) $100 \mathrm{~m} / \mathrm{s}$
(b) $200 \mathrm{~m} / \mathrm{s}$
(c) $600 \mathrm{~m} / \mathrm{s}$
(d) $700 \mathrm{~m} / \mathrm{s}$

VS
Vivek Singh
Numerade Educator
01:39

Problem 21

It was calculated that a shell when fired from a gun with a certain velocity and at an angle of elevation $\frac{5 \pi}{36}$ rad should strike a given target. In actual practice, it was found that a hill just prevented the trajectory. At what angle of elevation should the gun be to hit the target?
(a) $\frac{5 \pi}{36} \mathrm{rad}$
(b) $\frac{11 \pi}{36} \mathrm{rad}$
(c) $\frac{7 \pi}{36} \mathrm{rad}$
(d) $\frac{13 \pi}{36} \mathrm{rad}$

Aman Gupta
Aman Gupta
Numerade Educator
00:52

Problem 22

Two projectiles thrown from the same point at angles $60^{\circ}$ and $30^{\circ}$ with the horizontal attain the same height. The ratio of their initial velocities is
(a) 1
(b) 2
(c) $\sqrt{3}$
(d) $\frac{1}{\sqrt{3}}$

Hast Aggarwal
Hast Aggarwal
Numerade Educator
00:53

Problem 23

A projectile is thrown at angle $\beta$ with vertical. It reaches a maximum height $H$. The time taken to reach the highest point of its path is
(a) $\sqrt{\frac{H}{g}}$
(b) $\sqrt{\frac{2 H}{g}}$
(c) $\sqrt{\frac{H}{2 \tau}}$
(d) $\sqrt{\frac{2 H}{a_{-m} f}}$

Hast Aggarwal
Hast Aggarwal
Numerade Educator
01:00

Problem 24

A cricket ball is hit at $30^{\circ}$ with the horizontal with kinetic energy $E_{k}$. What is the kinetic energy at the highest point?
(a) $\frac{E_{1}}{2}$
(b) $\frac{3 E_{1}}{4}$
(c) $\frac{E_{\mathrm{b}}}{4}$
(d) Zero

Varsha Aggarwal
Varsha Aggarwal
Numerade Educator
06:03

Problem 25

A particle is projected with a velocity of $30 \mathrm{~m} / \mathrm{s}$, at an angle $\theta_{0}=\tan ^{-1}\left(\frac{3}{4}\right)$. After $1 \mathrm{~s}$, the particle is moving at an angle $\theta$ to the horizontal, where $\tan \theta$ will be equal to $\left(g=10 \mathrm{~m} / \mathrm{s}^{2}\right)$
(a) $]$
(b) 2
(c) $\frac{1}{2}$
(d) $\frac{1}{3}$

Vishal Gupta
Vishal Gupta
Numerade Educator
01:11

Problem 26

When a projectile is projected at a certain angle with the horizontal, its horizontal range is $R$ and time of flight is $T_{1}$. When the same projectile is throwing with the same speed at some other angle with the horizontal, its horizontal range is $R$ and time of flight is $T_{2}$. The produet of $T_{1}$ and $T_{2}$ is
(a) $\frac{R}{g}$
(b) $\frac{2 R}{g}$
(c) $\frac{3 R}{g}$
(d) $\frac{4 R}{g}$

Hast Aggarwal
Hast Aggarwal
Numerade Educator
02:56

Problem 27

A projectile of mass $m$ is thrown with a velocity $y$ making an angle of $45^{\circ}$ with the horizontal. The change in momentum from departure to arrival along vertical direction, is
(a) $2 \mathrm{mv}$
(b) $\sqrt{2} \mathrm{mv}$
(c) $m$ v
(d) $\frac{m \mathrm{v}}{2}$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
01:51

Problem 28

Two stones thrown at different angles have same initial velocity and same range. If $H$ is the maximum height attained by one stone thrown at an angle of $30^{\circ}$, then the maximum height attained by the other stone is
(a) $\frac{H}{2}$
(b) $\underline{H}$
(c) $2 H$
(d) $3 \mathrm{H}$

Nishant Kumar
Nishant Kumar
Numerade Educator
01:21

Problem 29

A projectile shot into air at some angle with the horizontal has a range of $200 \mathrm{~m}$. If the time of flight is 5 s, then the horizontal component of the velocity of the projectile at the highest point of trajectory is
(a) $40 \mathrm{~ms}^{-1}$
(b) $0 \mathrm{~ms}^{-1}$
(c) $9.8 \mathrm{~ms}^{-1}$
(d) equal to the velocity of projection of the projectile

Satpal Satpal
Satpal Satpal
Numerade Educator
02:10

Problem 30

The kinetic energy of a project at the height point is half of the initial kinetic energy. What is the angle of projection with the horizontal?
[a) $3 \overline{0^{\circ}}$
(b) $45^{*}$
(c) $6 \overline{0^{n}}$
(d) $90^{*}$

Narendra Kumar
Narendra Kumar
Numerade Educator
02:20

Problem 31

A ball is projected from a certain point on the surface of a planet at a certain angle with the horizontal surface. The horizontal and vertical displacement $x$ and $y$ vary with time $t$ in second as $x=10 \sqrt{3} t$ and $y=10 t-t^{2}$. The maximum height attained by the ball is
(a) $100 \mathrm{~m}$
(b) $75 \mathrm{~m}$
(c) $50 \mathrm{~m}$
(d) $25 \mathrm{~m}$

Satpal Satpal
Satpal Satpal
Numerade Educator
00:52

Problem 32

A projectile $A$ is thrown at an angle of $30^{\circ}$ to the horizontal from point $P$. At the same time, another projectile $B$ is thrown with velocity $v^{2}$ upwards from the point $Q$ vertically below the highest point. For $B$ to collide with $A, \frac{v_{2}}{\text { should be }}$ $v_{1}$
(a) 1
(b) 2
(c) $\frac{1}{2}$
(d) 4

Hast Aggarwal
Hast Aggarwal
Numerade Educator
01:00

Problem 33

For a projectile thrown into space with a speed $v$, the horizontal range is $\frac{\sqrt{3} v^{2}}{2 g} .$ The vertical range is $\frac{v^{2}}{8 g}$. The angle which the projectile makes with the horizontal initially is
(a) $15^{*}$
(b) $30^{*}$
(c) $45^{\circ}$
[d) $60^{\circ}$

Varsha Aggarwal
Varsha Aggarwal
Numerade Educator
02:05

Problem 34

The velocity of projection of an oblique projectile is $(6 \hat{\mathbf{i}}+\mathbf{8} \hat{\mathbf{j}}) \mathrm{ms}^{-1}$. The horizontal range of the projectile
is
(a) $4.9 \mathrm{~m}$
(b) $9.6 \mathrm{~m}$
(c) $19.6 \mathrm{~m}$
(d) $14 \mathrm{~m}$

Vysakh M
Vysakh M
Numerade Educator
01:19

Problem 35

A body is projected at an angle $\theta$ to the horizontal with kinetic energy $E_{k}$ - The potential energy at the highest point of the trajectory is
[a) $E_{\mathrm{i}}$
(b) $E_{1} \cos ^{2} \theta$
(c) $E_{i} \sin ^{2} \theta$
(d) $E_{\text {i }} \tan ^{2} 0$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
02:23

Problem 36

Two projectiles $A$ and $B$ are thrown with velocities $v$ and $\frac{v}{2}$ respectively. They have the same range. If $B$ is thrown at an angle of $15^{\circ}$ to the horizontal, A must have been thrown at an angle
(a) $\sin ^{-1}\left(\frac{1}{16}\right)$
(b) $\sin ^{-1}\left(\frac{1}{4}\right)$
(c) $2 \sin ^{-1}\left(\frac{1}{4}\right)$
(d) $\frac{1}{2} \sin ^{-1}\left(\frac{1}{8}\right)$

Vishal Gupta
Vishal Gupta
Numerade Educator
07:37

Problem 37

A particle slides down a frictionless parabolie $\left(y=x^{2}\right)$ track $(A-B-C)$ starting from rest at point $A$. Point $B$ is at the vertex of parabola and point $C$ is at a height less than that of point $A$. After $C_{n}$ the particle moves freely in air as a projectile. If the particle reaches highest point at $P$, then INCERT Exemplar]
(a) KE at $P=K E$ at $B$
(b) height at $P$ meight at $A$
(c) total energy at $P=$ total energy at $A$
(d) time of travel from $A$ to $B$ me of travel from $B$ to $P_{\text {. }}$

Suman Saurav Thakur
Suman Saurav Thakur
Numerade Educator
00:26

Problem 38

The horizontal range of an oblique projectile is equal to the distance through which a projectile has to fall freely from rest to acquire a velocity equal to the velocity of projection in magnitude. The angle of projection is
(a) $15^{\circ}$
(b) $60^{*}$
(c) $45^{\circ}$
(d) $3 \overline{0^{*}}$

Hast Aggarwal
Hast Aggarwal
Numerade Educator
01:11

Problem 39

A projectile is thrown with velocity v making an angle $\theta$ with the horizontal. It just crosses the tops of two poles, each of height $h$, after $1 \mathrm{~s}$ and 3 s respectively. The time of flight of the projectile is
(a) $1 \mathrm{~s}$
(b) $3 \mathrm{~s}$
(c) $4 \mathrm{~s}$
(d) $7.8 \mathrm{~s}$

Hast Aggarwal
Hast Aggarwal
Numerade Educator
01:14

Problem 40

Two stones are projected so as to reach the same distance from the point of projection on a horizontal surface. The maximum height reached by one exceeds the other by an amount equal to half the sum of the height attained by them. Then, angle of projection of the stone which attains smaller height is
[a] $45^{\circ}$
(b) $60^{\circ}$
(c) $3 \overline{0^{*}}$
(d) $\tan ^{-1}(3 / 4)$

Varsha Aggarwal
Varsha Aggarwal
Numerade Educator
02:01

Problem 41

Two particles are simultaneously projected in opposite directions horizontally from a given point in space whose gravity $g$ is uniform. If $u_{1}$ and $u_{2}$ be their initial speeds, then the time $t$ after which their velocites are mutually perpendicular is given by
(a) $\frac{\sqrt{u_{\mu_{2}}}}{g}$
(b) $\frac{\sqrt{\|_{1}^{2}+t_{2}^{2}}}{g}$
(c) $\frac{g}{\sqrt{u_{1}\left(u_{1}+u_{2}\right)}}{g}$
(d) $\frac{\sqrt{u_{1}\left(u_{1}+u_{2}\right)}}{g}$

Mahendra K
Mahendra K
Numerade Educator
02:07

Problem 42

A plane surface is inclined making an angle $\theta$ with the horizontal. From the bottom of this inclined plane, a bullet is fired with velocity $v .$ The maximum possible range of the bullet on the inclined plane is
(a) $\frac{v^{2}}{g}$
(b) $\frac{v^{2}}{g(1+\sin \theta)}$
(c) $\frac{v^{2}}{g(1-\sin \theta)}$
(d) $\frac{v^{2}}{g\left(1+\sin \theta^{2}\right.}$

Narayan Hari
Narayan Hari
Numerade Educator
01:30

Problem 43

A projectile is fired with a velocity $v$ at an angle $\theta$ with the horizontal. The speed of the projectile when its direction of motion makes an angle $\beta$ with the horizontal is
(a) $v \cos \theta$
(b) $v \cos \theta \cos \beta$
(c) $v \cos \theta \sec \beta$
(d) $v \cos \theta \tan \beta$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
02:15

Problem 44

A ball is projected up an incline of $30^{\circ}$ with a velocity of $30 \mathrm{~ms}^{-1}$ at an angle of $30^{\circ}$ with reference to the inclined plane from the bottom of the inclined plane. If $g=10 \mathrm{~ms}^{-2}$, then the range on the inclined plane is
(a) $12 \mathrm{~m}$
(b) $60 \mathrm{~m}$
(c) $120 \mathrm{~m}$
(d) $600 \mathrm{~m}$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
02:40

Problem 45

A cricketer can throw a ball to a maximum horizontal distance of $100 \mathrm{~m}$. How much high above the ground can the cricketer throw the same ball? INCERT Exemplar]
(a) $40 \mathrm{~m}$
(b) $45 \mathrm{~m}$
[c) $500 \mathrm{~m}$
(d) $50 \mathrm{~m}$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
02:58

Problem 46

A piece of marble is projected from earth's surface with velocity of $50 \mathrm{~ms}^{-1}, 2 \mathrm{~s}$ later it just clears a wall $5 \mathrm{~m}$ high. What is the angle of projection?
(a) $45^{\circ}$
(b) $30^{*}$
(c) $60^{\circ}$
(d) None of these

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
01:19

Problem 47

A body is projected with speed $v \mathrm{~ms}^{-1}$ at angle $\theta$. The kinetic energy at the highest point is half of the initial kinetic energy. The value of $\theta$ is
(a) $30^{\circ}$
(b) $45^{\circ}$
(c) $60^{\circ}$
(d) $90^{\circ}$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
01:30

Problem 48

A ball is projected with velocity $u$ at an angle $\alpha$ with horizontal plane. Its speed when it makes an angle $\beta$ with the horizontal is
(a) $u \cos \alpha$
(b) $\frac{u}{\cos \beta}$
(c) $u \cos \alpha \cos \beta$
(d) $\frac{u \cos c}{\cos \beta}$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
01:22

Problem 49

The angle of projection of a projectile for which the horizontal range and maximum height are equal to
(a) $\tan ^{-1}(2)$
(b) $\tan ^{-1}(4)$
(c) $\cot ^{-1}(2)$
(d) $60^{\circ}$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
02:19

Problem 50

A particle is projected from horizontal making an angle $60^{\circ}$ with initial velocity $40 \mathrm{~ms}^{-1}$. The time taken by the particle to make angle $45^{\circ}$ from horizontal, is
(a) $15 \mathrm{~s}$
(b) $2.0 \mathrm{~s}$
(c) $20 \mathrm{~s}$
(d) $1.5 \mathrm{~s}$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
05:47

Problem 51

Two bodies are projected from the same point with equal speeds in such directions that they both strike the same point on a plane whose inclination is $\beta$. If $\alpha$ be the angle of projection of the first body with the horizontal the ratio of their times of flight is
(a) $\frac{\cos \alpha}{\sin (\alpha+\beta)}$
(b) $\frac{\sin (\alpha+\beta)}{\cos \alpha}$
(c) $\frac{\cos \alpha}{\sin (\alpha-\beta)}$
(d) $\frac{\sin (\alpha-\beta)}{\cos \alpha}$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
07:10

Problem 52

A particle is projected with velocity $2 \sqrt{g h}$ so that it just clears two walls of equal height $h$, which are at a distance of $2 h$ from each other. What is the time interval of passing between the two walls?
(a) $\frac{2 h}{g}$
(b) $\sqrt{\frac{g h}{g}}$
(c) $\sqrt{\frac{h}{g}}$
(d) $2 \sqrt{\frac{h}{g}}$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
04:01

Problem 53

A projectile is thrown with a velocity of $10 \mathrm{~m} / \mathrm{s}$ at an angle $60^{\circ}$ with horizontal. The interval between the moment when speed is $\sqrt{5} g \mathrm{~m} / \mathrm{s}$, is $\left(g=10 \mathrm{~m} / \mathrm{s}^{2}\right)$.
[al $1 \underline{5}$
(b) $3 \mathrm{~s}$
(c) 25
(d) $4 \mathrm{~s}$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
03:15

Problem 54

A particle is projected from the ground with an initial speed of $v$ at an angle $\theta$ with horizontal. The average velocity of the particle between its point of projection and highest point of trajectory is
(a) $\frac{v}{2} \sqrt{1+2 \cos ^{2} \theta}$
(b) $\frac{v}{2} \sqrt{1+\cos ^{2} \theta}$
(c) $\frac{v}{2} \sqrt{1+3 \cos ^{2} \theta}$
(d) $v \cos \theta$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
02:07

Problem 55

A body of mass $m$ is thrown upward at an angle $\theta$ with the horizontal with velocity $v$. While rising up the velocity of the mass after $t$ second will be
(a) $\sqrt{[v \cos \theta)^{2}+(v \cdot \sin \theta)^{2}}$
(b) $\sqrt{(v \cos \theta-v \sin \theta)^{2}-g t}$
(c) $\sqrt{v^{2}+g^{2} t^{2}-(2 v \sin \theta) g t}$
(d) $\sqrt{v^{2}+g^{2} t^{2}-(2 v \cos \theta) g t}$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
02:17

Problem 56

A projectile is thrown at an angle $\theta$ such that it is just able to eross a vertical wall as its highest point as shown in the figure. The angle $\theta$ at which the projectile is thrown is given by (a) $\tan ^{-1}\left(\frac{1}{\sqrt{3}}\right)$,
(b) $\tan ^{-1} \sqrt{3}$
(c) $\tan ^{-1}\left(\frac{2}{\sqrt{3}}\right)$
(d) $\tan ^{-1}\left(\frac{\sqrt{3}}{2}\right)$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
04:48

Problem 57

A particle is projected with speed $v$ at an angle $\left(0<0<\frac{\pi}{2}\right)$ above the horizontal from a height $H$ above the ground. If $v=$ speed with which particle hits the ground and $t=$ time taken by particle to reach ground, then
(a) as $\theta$ increases, $v$ decreases and $t$ increase
(b) as $\theta$ increases, $v$ increases and $t$ increases
(c) as $\theta$ increases, $v$ remains same and $t$ increases
(d) as $\theta$ increases, $v$ remains same and $t$ decreases

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
03:45

Problem 58

Two inclined planes are located as shown in figure. A particle is projected from the foot of one frietionless plane along its line with a velocity sufficient to earry it to top after which the particle slides down the other frictionless inclined plane. The total time it will take to reach the point $C$ is
(a) $2 \mathrm{~s}$
(b) $3 \mathrm{~s}$
(c) $2 \sqrt{2} \mathrm{~s}$
(d) 4 s

Mahendra K
Mahendra K
Numerade Educator
02:11

Problem 59

The equation of motion of a projectile are given by $x=36 t .$ If and $2 y=96 t-9.8 t^{2} \mathrm{~m}$. The angle of projectile is
(a) $\sin ^{-1}\left(\frac{4}{5}\right)$
(b) $\sin ^{-1}\left(\frac{3}{5}\right)$
(c) $\sin ^{-1}\left(\frac{4}{3}\right)$
(d) $\sin ^{-1}\left(\frac{3}{4}\right)$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
01:15

Problem 60

Trajectories of two projectiles are shown in figure. Let $T_{1}$ and $T_{2}$ be the time periods and $u_{1}$ and $u_{2}$ their speeds of projection. Then,
(a) $T_{2}>T_{1}$
(b) $T_{1}=T_{2}$
(c) $u_{1}>u_{2}$
(d) $u_{1}<u_{2}$

Narayan Hari
Narayan Hari
Numerade Educator
00:52

Problem 61

A projectile $A$ is thrown at an angle $30^{\circ}$ to the horizontal from point $P .$ At the same time another projectile $B$ is thrown with velocity $v_{2}$ upwards from the point Qvertically below the highest point $A$ would reach. For $B$ to collide with $A$ the ratio $\frac{b_{2}}{\text { should be }}$ $v_{1}$
(a) $\frac{\sqrt{3}}{2}$
(b) 2
(c) $\frac{1}{2}$
(d) $\frac{2}{\sqrt{3}}$

Hast Aggarwal
Hast Aggarwal
Numerade Educator
03:48

Problem 62

A fighter plane enters inside the enemy territory, at time $t=0$ with velocity $v_{0}=250 \mathrm{~ms}^{-1}$ and moves horizontally with constant acceleration $a=20 \mathrm{~ms}^{-2}$ (see figure). An enemy tank at the border, spot the plane and fire shots at an angle $\theta=60^{\circ}$ with the horizontal and with velocity $u=600 \mathrm{~ms}^{-1}$. At what altitude $H$ of the plane it can be hit by the shot?
(a) $1500 \sqrt{3} \mathrm{~m}$
(b) $125 \mathrm{~m}$
(c) $1400 \mathrm{~m}$
(d) $2473 \mathrm{~m}$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
06:59

Problem 63

An aircraft, diving at an angle of $53.0^{\circ}$ with the vertical releases a projectile at an altitude of $730 \mathrm{~m}$. The projectile hits the ground $5.00 \mathrm{~s}$ after being released. What is the speed of the aircraft?
(a) $282 \mathrm{~ms}^{-1}$
(b) $202 \mathrm{~ms}^{-1}$
(c) $182 \mathrm{~ms}^{-1}$
(d) $102 \mathrm{~ms}^{-1}$

Donald Albin
Donald Albin
Numerade Educator
01:50

Problem 64

A particle $A$ is projected from the ground with an initial velocity of $10 \mathrm{~ms}^{-1}$ at an angle of $60^{\circ}$ with horizontal. From what height $h$ should an another particle $B$ be projected horizontal with veloeity $5 \mathrm{~ms}^{-1}$ go that both the particles collide with velocity $5 \mathrm{~ms}^{-1}$ so that both the particles collide on the ground at point $C$ if both are projected simultaneously? $\left(g=10 \mathrm{~ms}^{-2}\right)$
(a) $10 \mathrm{~m}$
(b) $30 \mathrm{~m}$
[c) $15 \mathrm{~m}$
(d) $25 \mathrm{~m}$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
02:01

Problem 65

A very broad elevator is going up vertically with a constant acceleration of $2 \mathrm{~ms}^{-2}$. At the instant when its velocity is $4 \mathrm{~ms}^{-1}$ a ball is projected from the floor of the list with a speed of $4 \mathrm{~ms}^{-1}$ relative to the floor at an elevation of $30^{\circ}$. The time taken by the ball to return the floor is $\left(g=10 \mathrm{~ms}^{-2}\right)$
(a) $1 / 2 s$
(b) $1 / 3 \mathrm{~s}$
(c) $1 / 4 \mathrm{~s}$
(d) $1 \mathrm{~s}$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator
01:57

Problem 66

A projectile is fired at an angle of $30^{\circ}$ to the horizontal such that the vertical component of its initial velocity is $80 \mathrm{~ms}^{-1}$, Its time of flight is $T$. Its velocity at $t=\frac{T}{4}$ has a magnitude of nearly
(a) $200 \mathrm{~ms}^{-1}$
(b) $300 \mathrm{~ms}^{-1}$
(c) $140 \mathrm{~ms}^{-1}$
(d) $100 \mathrm{~ms}^{-1}$

Varsha Aggarwal
Varsha Aggarwal
Numerade Educator
02:53

Problem 67

A car is moving rectilinearly on a horizontal path with acceleration $a_{0 .}$ A person sitting inside the car observes that an insect $S$ is crawling up the screen with an acceleration $a .$ If $\theta$ is the inclination of the sereen with the horizontal the acceleration of the insect
[a) parallel to screen is $a_{0} \cos \theta$
(b) along the horizontal is $a_{0}-a \cos \theta$
(c) perpendiculat to screen is $a_{0} \sin \theta$
(d) perpendicular to screen is $a_{0} \tan \theta$

Keshav Singh
Keshav Singh
Numerade Educator
01:29

Problem 68

A particle is projected from the ground at an angle of $60^{\text {n }}$ with horizontal with speed $u=20 \mathrm{~ms}^{-1}$. The radius of curvature of the path of the particle, when its velocity makes an angle of $30^{\circ}$ with horizontal is $\left(g=10 \mathrm{~ms}^{-2}\right)$
(a) $10.6 \mathrm{~m}$
(b) $12.8 \mathrm{~m}$
(c) $15.4 \mathrm{~m}$
(d) $24.2 \mathrm{~m}$

Dheeraj Sharma
Dheeraj Sharma
Numerade Educator