Motion · Physics · JEE Advanced
Numerical
1
A ball is thrown from the location $\left(x_0, y_0\right)=(0,0)$ of a horizontal playground with an initial speed $v_0$ at an angle $\theta_0$ from the $+x$-direction. The ball is to be hit by a stone, which is thrown at the same time from the location $\left(x_1, y_1\right)=(L, 0)$. The stone is thrown at an angle $\left(180-\theta_1\right)$ from the $+x$-direction with a suitable initial speed. For a fixed $v_0$, when $\left(\theta_0, \theta_1\right)=\left(45^{\circ}, 45^{\circ}\right)$, the stone hits the ball after time $T_1$, and when $\left(\theta_0, \theta_1\right)=\left(60^{\circ}, 30^{\circ}\right)$, it hits the ball after time $T_2$. In such a case, $\left(T_1 / T_2\right)^2$ is ______.
JEE Advanced 2024 Paper 2 Online
2
A person of height $1.6 \mathrm{~m}$ is walking away from a lamp post of height $4 \mathrm{~m}$ along a straight path on the flat ground. The lamp post and the person are always perpendicular to the ground. If the speed of the person is $60 \mathrm{~cm} \mathrm{~s}^{-1}$, the speed of the tip of the person's shadow on the ground with respect to the person is ____________ $\mathrm{cm}~ \mathrm{s}^{-1}$.
JEE Advanced 2023 Paper 1 Online
3
A projectile is fired from horizontal ground with speed $v$ and projection angle $\theta$. When the acceleration due to gravity is $g$, the range of the projectile is $d$. If at the highest point in its trajectory, the projectile enters a different region where the effective acceleration due to gravity is $g^{\prime}=\frac{g}{0.81}$, then the new range is $d^{\prime}=n d$. The value of $n$ is ___________ .
JEE Advanced 2022 Paper 1 Online
4
A ball is thrown from ground at an angle $$\theta $$ with horizontal and with an initial speed u0. 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 V1. After hitting the ground, the ball rebounds at the same angle $$\theta $$ but with a reduced speed of $${{{u_0}} \over \alpha }$$. 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 V1, the value of $$\alpha $$ is ..................
JEE Advanced 2019 Paper 2 Offline
5
A ball is projected from the ground at an angle of $${45^o}$$ 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 $${30^o}$$ with the horizontal surface. The maximium height it reaches after the bounce, in metres, is ______________.
JEE Advanced 2018 Paper 2 Offline
6
Airplanes A and B are flying with constant velocity in the same vertical plane at angles $$30^\circ $$ and $$60^\circ $$ with
respect to the horizontal respectively as shown in the figure. The speed of A is $$100\sqrt 3 $$ m/s. At time t = 0 s, an observer in A finds B at a distance of 500 m. This observer sees B moving with a constant velocity
perpendicular to the line of motion of A. If at t = t0, A just escapes being hit by B, t0 in seconds is
JEE Advanced 2014 Paper 1 Offline
7
A rocket is moving in a gravity free space with a constant
acceleration of 2 ms–2 along + x direction (see figure). The
length of a chamber inside the rocket is 4 m. A ball is
thrown from the left end of the chamber in + x direction
with a speed of 0.3 ms–1 relative to the rocket. At the same
time, another ball is thrown in - x direction with a speed of
0.2 ms–1 from its right end relative to the rocket. The time in
seconds when the two balls hit each other is
JEE Advanced 2014 Paper 1 Offline
8
A train is moving along a straight line with a constant acceleration 'a'. A boy standing in the train throws a
ball forward with a speed of 10 m/s, at an angle of $$60^\circ $$ to the horizontal. The boy has to move forward by
1.15 m inside the train to catch the ball back at the initial height. The acceleration of the train, in m/s2, is
IIT-JEE 2011 Paper 2 Offline
MCQ (More than One Correct Answer)
1
Starting at time t = 0 from the origin with speed 1 ms-1, a particle follows a two-dimensional trajectory in the x-y plane so that its coordinates are related by the equation $$y = {{{x^2}} \over 2}$$. The x and y components of its acceleration are denoted by ax and ay, respectively. Then
JEE Advanced 2020 Paper 2 Offline
2
The coordinates of a particle moving in a plane are given by x(t) = a cos(pt) and y(t) = b sin(pt) where a, b (< a) and p are positive constants of approprite dimensions. Then
IIT-JEE 1999 Screening
3
A particle of mass m moves on the x-axis as follows: it starts from rest at t = 0 from the point x = 0, and come to rest at t = 1 at the point x = 1. NO other information is available about its motion at intermediate times ( 0 < t < 1 ). If $$\alpha $$ denotes the instantaneous acceleration of the particle, then:
IIT-JEE 1993
4
A particle is moving eastwards with a velocity of 5 m/s. In 10s the velocity changes to 5 m/s northwards. The average acceleration in this time is
IIT-JEE 1982
MCQ (Single Correct Answer)
1
Consider an expanding sphere of instantaneous radius R whose total mass remains constant. The expansion is such that the instantaneous density $$\rho $$ remains uniform throughout the volume. The rate of fractional change in density $$\left( {{1 \over \rho } {{d\rho } \over {dt}}} \right)$$ is constant. The velocity $$v$$ of any point on the surface of the expanding sphere is proportional to
JEE Advanced 2017 Paper 2 Offline
2
Three vectors $$\overrightarrow P ,\overrightarrow Q $$ and $$\overrightarrow R $$ are shown in the figure. Let $$S$$ be any point on the vector $$\overrightarrow R .$$ The distance between the points $$P$$ and $$S$$ is $$b\left| {\overrightarrow R } \right|.$$ The general relation among vectors $$\overrightarrow P ,\overrightarrow Q $$ and $$\overrightarrow S $$ is :
JEE Advanced 2017 Paper 2 Offline
3
STATEMENT-1: For an observer looking out through the window of a fast moving train, the nearby objects appear to move in the
opposite direction to the train, while the distant objects appear to be stationary.
STATEMENT-2: If the observer and the object are moving at velocities $${\overrightarrow v _1}$$ and $${\overrightarrow v _2}$$ respectively with reference to a laboratory frame, the velocity of the object with respect to the observer is $${\overrightarrow v _2}$$ - $${\overrightarrow v _1}$$.
IIT-JEE 2008 Paper 2 Offline
4
A particle starts sliding down a frictionless inclined plane. If Sn is the distance traveled by it from time t = n - 1 sec to t = n sec, the ratio Sn / Sn+1 is
IIT-JEE 2004 Screening
5
A body starts from rest at time t = 0, the acceleration time graph is
shown in the figure. The maximum velocity attained by the body
will be
IIT-JEE 2004 Screening
6
A boat which has a speed of 5 km/hr in still water crosses a river of width 1 km along the shortest possible path in 15 minutes. The velocity of the river water in km/hr is
IIT-JEE 1988
7
A river is flowing from west to east at a speed of 5 meters per minute. A man on the south bank of the river, capable of swimming at 10 meters per minute in still water, wants to swim across the river in the shortest time. He should swim in a direction
IIT-JEE 1983
Subjective
1
Two guns, situated on the top of a hill of height 10 m, fire one shot each with the same speed $$5\sqrt 3 $$ m s-1 at some interval of time. One gun fires horizontally and other fires upwards at an angle of $$60^\circ $$ with the horizontal. The shots collide in air at a point P. Find
(i) the time interval between the firings, and
(ii) the coordinates of the point P.
Take origin of the coordinate system at the foot of the hill right below the muzzle and trajectories in x-y plane.IIT-JEE 1996
2
Answer the following giving reason in brief:
Is the time variation of position, shown in the figure observed in nature?
IIT-JEE 1979
3
The dispalcement x of particle moving in one direction, under the action of a constant force is related to the time t by the equation $$t = \sqrt x + 3$$
where x is in meters and t in seconds. Find
where x is in meters and t in seconds. Find
(i) The displacement of the particle when its velocity is zero, and
(ii) The work done by the force in the first 6 seconds.
IIT-JEE 1979
4
A car accelerates from rest at a constant rate $$\alpha $$ for some time after which it decelerates at a constant rate $$\beta $$ to come to rest. If the total time lapse is t seconds, evaluate.
(i) maximum velocity reached, and
(ii) the total distance travelled.
IIT-JEE 1978
True or False
1
Two identical trains are moving on rails along the equator on the earth in opposite directions with the same speed. They will exert the same pressure on the rails.
IIT-JEE 1985
2
A projectile fired from the ground follows a parabolic path. The speed of the projectile is minimum at the top of its path.
IIT-JEE 1984
3
Two balls of different masses are thrown vertically upwards with the same speed. They pass through the point of projection in their downward motion with the same speed. (Neglect air resistance)
IIT-JEE 1983
Fill in the Blanks
1
Four person K, L, M, N are initially at the four corners of a square of side d. Each person now moves with a uniform speed v in such a way that K always moves directly towards L, L directly towards M, M directly towards N, and N directly towards K. The four person will meet at a time _____________.
IIT-JEE 1984
2
A particle moves in a circle of radius R. In half the period of revolution its displacement is ________ and distance covered is _________.
IIT-JEE 1983