Question 1 :
If the time of flight of a projectile is doubled, what happens to the maximum height attained?
Question 2 :
A particle reaches its highest point when it has covered exactly one half of its horizontal range. The corresponding point on the vertical displacement-time graph is characterised by
Question 3 :
A projectile is fired from level ground at an angle {tex} \theta {/tex} above the horizontal. The elevation angle {tex} \phi {/tex} of the highest point as seen from the launch point is related to {tex} \theta {/tex} by the relation
Question 4 :
A ball is thrown at different angles with the same speed {tex} u {/tex} and from the same point and it has the same range in both the cases. If {tex} y _ { 1 } {/tex} and {tex} y _ { 2 } {/tex} are the heights attained in the two cases, then {tex} y _ { 1 } + y _ { 2 } {/tex} is equal to<br>
Question 5 :
A ball is dropped from a height of {tex} 49 \mathrm { m } {/tex}, the wind blows horizontally and imparts a constant acceleration of {tex} 4.90 \mathrm { ms } ^ { - 2 } {/tex} to the ball. Choose the correct statement(s)
Question 6 :
The range {tex} R {/tex} of projectile is same when its maximum heights are {tex} h _ { 1 } {/tex} and {tex} h _ { 2 } . {/tex} What is the relation between {tex} R , h _ { 1 } , {/tex} and {tex} h _ { 2 } ? {/tex}
Question 7 :
In the second part of question {tex} 56 , {/tex} the time taken to return to the ground from the maximum height
Question 8 :
The safe speed to avoid skidding on the unbanked curve is
Question 10 :
A projectile is given an initial velocity of {tex} \hat { \imath } + 2 \hat { \jmath } {/tex}. The cartesian equation of its path is {tex} \left( \mathrm { g } = 10 \mathrm { ms } ^ { - 2 } \right) {/tex}
Question 11 :
If air resistance is not considered in a projectile motion, the horizontal motion takes place with
Question 12 :
Which of the following matching represents the body moving with constant acceleration?
Question 13 :
If {tex} a _ { r } {/tex} and {tex} a _ { t } {/tex} represent radial and tangential acceleration, the motion of a particle will be circular if
Question 14 : A particle is moving along a straight line whose velocity displacement graph is shown in Fig<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Advanced/5e37f73a8e34721b52b49367"><br>What is the acceleration when displacement is {tex} 3 \mathrm { m } ? {/tex}
Question 15 :
A particle is moving along a circular path. The angular velocity, linear velocity, angular acceleration, and centripetal acceleration of the particle at any instant respectively are {tex} \vec { \omega } , \vec { v } , \vec { \alpha } , {/tex} and {tex} \vec { a } _ { c } . {/tex} Which of the following relations is not correct?<br>
Question 17 : In 1.0{tex}\mathrm { s }{/tex} , a particle goes from point A to point B , moving in a semicircle of radius 1.0{tex}\mathrm { m }{/tex} (see Figure). The magnitude of the average velocity <br> <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Advanced/5e26ebae4fb21d2dc85e8a2c' />
Question 18 :
A stationary person observes that rain is falling vertically down at {tex} 30 \mathrm { kmh } ^ { - 1 } {/tex}. A cyclist is moving up on an inclined plane making an angle {tex} 30 ^ { \circ } {/tex} with horizontal at {tex} 10 \mathrm { kmh } ^ { - 1 } {/tex}. In which direction should the cyclist hold his umbrella to prevent himself from the rain?
Question 19 :
A particle is projected at an angle {tex} \theta = 30 ^ { \circ } {/tex} with the horizontal, with a velocity of {tex} 10 \mathrm { ms } ^ { - 1 } . {/tex} Then
Question 20 :
A body is moving in a circular path with a constant speed. It has
Question 21 : A particle {tex} P {/tex} is sliding down a frictionless hemispherical bowl. It passes the point {tex} A {/tex} at {tex} t = 0 . {/tex} At this instant of time, the horizontal component of its velocity {tex} v . {/tex} A bead {tex} Q {/tex} of the same mass as {tex} P {/tex} is ejected from {tex} A {/tex} to {tex} t = 0 {/tex} along the horizontal string {tex} A B {/tex} (see figure) with the speed {tex} v {/tex}. Friction between the bead and the string may be neglected. Let {tex} t _ { p } {/tex} and {tex} t _ { Q } {/tex} be the respective time taken by {tex} P {/tex} and {tex} Q {/tex} to reach the point {tex} B {/tex}. Then<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Advanced/5e37f54d3df3381b1c3148e0"><br>
Question 22 :
A body of mass m projected at an angle {tex} \theta {/tex} with horizontal. Which of the following shows the correct matching for the position, velocity and acceleration of the body with respect to time?
Question 23 :
The point from where a ball is projected is taken as the origin of the coordinate axes. The {tex} x {/tex} and {tex} y {/tex} components of its displacement are given by {tex} x = 6 t{/tex} and {tex} y = 8 t - 5 t ^ { 2 } . {/tex} What is the velocity of projection?
Question 24 :
A river is flowing from west to east at a speed of 5 metres per minute, A man on the south bank of the river, capable of swimming at 10 metres per minute in still water, wants to swim across the river in the shortest time. He should swim in a direction
Question 25 :
A vector {tex} \vec {\mathrm A } {/tex} is rotated by a small angle {tex} \Delta \theta {/tex} radian {tex} ( \Delta \theta < < 1 ) {/tex} to get a new vector {tex} \overrightarrow { \mathrm { B } } {/tex}. In that case {tex} | \overrightarrow { \mathrm { B } } - \overrightarrow { \mathrm { A } } | {/tex} is :
Question 26 :
A particle undergoes uniform circular motion. About which point on the circle, will the angular momentum of the particle remain conserved?
Question 27 :
A particle is moving eastwards with a velocity of {tex} 5 \mathrm { m } / \mathrm { s } {/tex}. In {tex} 10 \mathrm { s } {/tex} the velocity changes to {tex} 5 \mathrm { m } / \mathrm { s } {/tex} northwards. The average acceleration in this time is
Question 28 :
What is the magnitude of the upward force on the rider?
Question 29 :
A car is moving in a circular horizontal track of radius {tex} 10 \mathrm { m } {/tex} with a constant speed of {tex} 10 \mathrm { m } / \mathrm { sec } . {/tex} A plumb bob is suspended from the roof of the car by a light rigid rod of length {tex} 1.00 \mathrm { m } {/tex}. The angle made by the rod with track is
Question 30 :
The speed of rain with respect to the stationary man is<br>
Question 31 :
A river is flowing from west to east at a speed of {tex} 5 \mathrm { m } / \mathrm { min } {/tex}. A man on the south bank of the river, capable of swimming at {tex} 10 \mathrm { m } / \mathrm { min } {/tex} in still water, wants to swim across the river in the shortest time. Finally he will move in a direction
Question 32 :
A projectile fired from the ground follows a parabolic path. The speed of the projectile is minimum at the top of its path.
Question 33 :
A ball is thrown upwards at an angle of {tex} 60 ^ { \circ } {/tex} to the horizontal. It falls on the ground at a distance of {tex} 90 \mathrm { m } . {/tex} If the ball is thrown with the same initial velocity at an angle {tex} 30 ^ { \circ } {/tex} it will fall on the ground at a distance of
Question 34 :
If {tex} A = 5 {/tex} units, {tex} B = 6 {/tex} units and {tex} | \overrightarrow { \mathrm { A } } \times \overrightarrow { \mathrm { B } } | = 15 {/tex} units, then what is the angle between {tex} \overrightarrow { \mathrm { A } } {/tex} and {tex} \overrightarrow { \mathrm { B } } ? {/tex}
Question 35 :
A car is moving horizontally along a straight line with a uniform velocity of {tex} 25 \mathrm { ms } ^ { - 1 } . {/tex} A projectile is to be fired from this car in such a way that it will return to it after it has moved {tex} 100 \mathrm { m } {/tex}. The speed of the projection must be
Question 36 :
An object moves along the {tex} x {/tex} -axis. Its {tex} x {/tex} -coordinates is given as a function of time as {tex} x = 7 t - 3 t ^ { 2 } \mathrm { m } , {/tex} where {tex} x {/tex} is in metres and {tex} t {/tex} is in seconds. Its average speed over the interval {tex} t = 0 {/tex} to {tex} t = 4 \mathrm { s } {/tex} is<br>
Question 37 :
The friction of air causes a vertical retardation equal to {tex} 10 \% {/tex} of the acceleration due to gravity (take {tex} \mathrm { g } = 10 \mathrm { ms } ^ { - 2 } {/tex} ). The maximum height will be decreased by
Question 38 :
A bird is flying towards north with a velocity {tex} 40 \mathrm { kmh } ^ { - 1 } {/tex} and a train is moving with velocity {tex} 40 \mathrm { kmh } ^ { - 1 } {/tex} towards east. What is the velocity of the bird noted by a man in the train?
Question 39 :
The maximum height reached by projectile is {tex} 4 \mathrm { m } {/tex}. The horizontal range is {tex} 12 \mathrm { m } {/tex}. The velocity of projection in {tex} \mathrm { ms } ^ { - 1 } {/tex} is ( {tex} \mathrm { g } {/tex} is acceleration due to gravity)
Question 40 : A bob of mass {tex} M {/tex} is suspended by a massless string of length {tex} L . {/tex} The horizontal velocity {tex} v {/tex} at position {tex} A {/tex} is just sufficient to make it reach the point {tex} B {/tex}. The angle {tex} \theta {/tex} at which the speed of the bob is half of that at {tex} A {/tex}, satisfies<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Advanced/5e37f6488e34721b52b49319"><br>
Question 41 : Consider a disc rotating in the horizontal plane with a constant angular speed m about its centre O. The disc has a shaded region on one side of the diameter and an unshaded region on the other side as shown in the figure. When the disc is in the orientation as shown, two pebbles P and Q are simultaneously projected at an angle towards R The velocity of projection is in the y-z plane and is same for both pebbles With respect to the disc. Assume that (i) they land back on the before the disc has completed 1/8 rotation, (ii) their range is less than half the disc radius, and (iii) {tex} \omega {/tex} remains constant throughout. Then<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Advanced/5e2049b53c34554a24698fc6">
Question 42 : Two trains having constant speeds of {tex} 40 \mathrm { kmh } ^ { - 1 } {/tex} and {tex} 60 \mathrm { kmh } ^ { - 1 } {/tex} respectively are heading towards each other on the same straight track<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Advanced/5e37f5078e34721b52b492ab"><br>A bird, when can fly with a constant speed of {tex} 30 \mathrm { kmh } ^ { - 1 } {/tex} flies off from one train when they are {tex} 60 \mathrm { km } {/tex} apart and heads directly for the other train. On reaching the other train, it flies back directly to the first and so forth. What is the total distance travelled by the bird before the two trains crash?
Question 43 :
A man holds an umbrella at {tex} 30 ^ { \circ } {/tex} with the vertical to keep himself dry. He, then, runs at a speed of {tex} 10 \mathrm { ms } ^ { - 1 } {/tex}, and find the rain drops to be hitting vertically. Study the following statements and find the correct options<br>I. Velocity of rain w.r.t. Earth is {tex} 20 \mathrm { ms } ^ { - 1 } {/tex} <br>II. Velocity of rain w.r.t. man is {tex} 10 \sqrt { 3 } \mathrm { ms } ^ { - 1 } {/tex} <br>III. Velocity of rain w.r.t. Earth is {tex} 30 \mathrm { ms } ^ { - 1 } {/tex} <br>IV. Velocity of rain w.r.t. man is {tex} 10 \sqrt { 2 } \mathrm { ms } ^ { - 1 } {/tex}<br>
Question 44 :
Wind is blowing in the north direction at speed of {tex} 2 \mathrm { ms } ^ { - 1 } {/tex}, which causes the rain to fall at some angle with the vertical. With what velocity should a cyclist drive so that the rain appears vertical to him:
Question 45 : The acceleration of a particle which moves along the positive {tex} x {/tex} -axis varies with its position as shown in Fig. If the velocity of the particle is {tex} 0.8 \mathrm { ms } ^ { - 1 } {/tex} at {tex}x = 0{/tex} , then velocity of the particle at {tex} x = 1.4 \mathrm { m } \text { is (in } \mathrm { ms } ^ { - 1 }) {/tex}<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Advanced/5e37f5623df3381b1c3148e6"><br>
Question 46 :
A ball is projected from the ground at angle {tex} \theta {/tex} with the horizontal. After 1s it is moving at angle {tex} 45 ^ { \circ } {/tex} with the horizontal and after 2s it is moving horizontally. What is the velocity of projection of the ball?
Question 47 :
A river flows with a speed more than the maximum speed with which a person can swim in still water. He intends to cross the river by the shortest possible path (i.e, he wants to reach the point on the opposite bank which directly opposite to the starting point). Which of the following is correct?
Question 48 :
A particle is projected with a certain velocity at an angle {tex} \alpha {/tex} above the horizontal from the foot of an inclined plane of inclination {tex} 30 ^ { \circ } . {/tex} If the particle strikes the plane normally, then {tex} \alpha {/tex} is equal to
Question 49 :
A uniform metallic spherical shell of inner radius R has a thickness t, such that $\frac{R}{t} $= 1000. The shell is kept in vacuum and also, there is a vacuum inside the shell. If absolute temperature of the metallic spherical shell is doubled, then the ratio of new radius to new thickness $\frac{R^{'}}{t^{'}} $ will be__
Question 50 : Three boys are running on a equitriangular track with the same speed {tex} 5 \mathrm { ms } ^ { - 1 } . {/tex} At start, they were at the three corners with velocity along indicated directions. The velocity of approach of any one of them towards another at {tex} t = 10 \mathrm { s } {/tex} equals<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Advanced/5e37f48820c6cd1b22465313"><br>
Question 51 : A body is projected up along a smooth inclined plane with velocity {tex} u {/tex} from the point {tex} A {/tex} as shown in Fig. The angle of inclination is {tex} 45 ^ { \circ } {/tex} and the top is connected to a well of diameter {tex} 40 \mathrm { m } {/tex}. If the body just manages to cross the well, what is the value of {tex} u {/tex} ? Length of inclined plane is {tex} 20 \sqrt { 2 } \mathrm { m } {/tex}<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Advanced/5e37f6888e34721b52b49328"><br>
Question 52 :
The displacement {tex} ( x ) {/tex} of a particle depends on time {tex} ( t ) {/tex} as {tex} x = \alpha t ^ { 2 } - \beta t ^ { 3 } {/tex}
Question 53 : A piece of wire is bent in the shape of a parabola {tex} y = k x ^ { 2 }{/tex} ( y -axis vertical) with a bead of mass {tex} m {/tex} on it. The bead can side on the wire without friction. It stays at the lowest point of the parabola when the wire is at rest. The wire is now accelerated parallel to the {tex} x {/tex} -axis with a constant acceleration {tex} a {/tex}. The distance of the new equilibrium position of the bead, where the bead can stay at rest with respect to the wire, from the {tex} y {/tex} - axis is<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Advanced/5e37f4403df3381b1c31488c">
Question 54 :
The coordinates of a particle moving in a plane are given by {tex} x ( t ) = a \cos ( \mathrm { pt } ) {/tex} and {tex} y ( t ) = b \sin ( \mathrm { pt } ) {/tex} where {tex} a , b ( < a ) {/tex} and {tex} p {/tex} are positive constants of appropriate dimensions. Then
Question 55 : Figure show that particle {tex} A {/tex} is projected from point {tex} P {/tex} with velocity {tex} u {/tex} along the plane and simultaneously another particle {tex} B {/tex} with velocity {tex} v {/tex} at an angle {tex} \alpha {/tex} with vertical. The particles collide at point {tex} Q {/tex} on the plane. Then<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Advanced/5e37f59c8e34721b52b492dc"><br>
Question 56 : Consider a disc rotating in the horizontal plane with a constant angular speed {tex} \omega {/tex} about its centre {tex} \mathrm { O } {/tex}. The disc has a shaded region on one side of the diameter and an unshaded region on the other side as shown in the figure. When the disc is in the orientation as shown, two pebbles {tex} P {/tex} and {tex} Q {/tex} are simultaneously projected at an angle towards {tex} R {/tex}. The velocity of projection is in the {tex} y {/tex} - {tex} z {/tex} plane and is same for both pebbles with respect to the disc. Assume that (i) they land back on the disc before the disc has completed {tex} 1 / 8 {/tex} rotation, (ii) their<br>range is less than half the disc radius, and (iii) {tex} \omega {/tex} remains constant throughout. Then<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Advanced/5f2cfd22bf25265a28d355fd">
Question 57 : A man swims from a point {tex} A {/tex} on one bank of width {tex} 100 \mathrm { m } {/tex}. When he swims perpendicular to the water current, he reaches the other bank {tex} 50 \mathrm { m } {/tex} downstream. The angle to the bank at which he should swim, to reach the directly opposite point {tex} B {/tex} on the other bank is<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Advanced/5e37f62820c6cd1b22465389"><br>
Question 58 :
Rain appears to fall vertically to a man walking at {tex} 3 \mathrm { kmh } ^ { - 1 } {/tex}, but when he changes his speed to double, the rain appears to fall at {tex} 45 ^ { \circ } {/tex} with vertical. Study the following statements and find which of them are correct<br>1. Velocity of rain is {tex} 2 \sqrt { 3 } \mathrm { kmh } ^ { - 1 } {/tex}<br> 2. The angle of fall of rain (with vertical) is {tex} \theta = \tan ^ { - 1 } \left( \frac { 1 } { \sqrt { 2 } } \right) {/tex}<br>3. The angle of fall of rain (with vertical) is {tex} \theta = \sin ^ { - 1 } \left( \frac { 1 } { \sqrt { 2 } } \right) {/tex} <br>4. Velocity of rain is {tex} 3 \sqrt { 2 } \mathrm { kmh } ^ { - 1 } {/tex}
Question 59 :
A projectile can have the same range {tex} R {/tex} for two angles of projection. It {tex} t _ { 1 } {/tex} and {tex} t _ { 2 } {/tex} are the times of flight in the two cases, then what is the product of two times of flight?
Question 60 :
A constant force acts on a mass m at rest. Velocity acquired in travelling a fixed distance is directly proportional to:
Question 61 : Three vectors {tex} \overrightarrow { \mathrm { P } } , \overrightarrow { \mathrm { Q } } {/tex} and {tex} \overrightarrow { \mathrm { R } } {/tex} are shown in the figure. Let {tex} \mathrm { S } {/tex} be anypoint on the vector {tex} \overrightarrow { \mathrm { R } } {/tex}. The distance between the points {tex} \mathrm { P } {/tex} and {tex} \mathrm { S } {/tex} is {tex} \mathrm { b } | \overrightarrow { \mathrm { R } } | {/tex}. The general relation among vectors {tex} \overrightarrow { \mathrm { P } } , \overrightarrow { \mathrm { Q } } {/tex} and {tex} \overrightarrow { \mathrm { S } } {/tex} is<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Advanced/5e2049bb3c34554a24698fcb">
Question 62 :
The maximum range of a projectile is {tex} 500 \mathrm { m } {/tex}. If the particle is thrown up a plane, which is inclined at an angle of {tex} 30 ^ { \circ } \mathrm { with } {/tex} the same speed, the distance covered by it along the inclined plane will be
Question 63 :
A ball rolls off the top of a staircase with a horizontal velocity {tex} u \mathrm { ms } ^ { - 1 } {/tex}. If the steps are {tex} h {/tex} metre high and {tex} b {/tex} metre wide, the ball will hit the edge of the nth step, if
Question 64 :
A projectile is thrown in the upward direction making an angle of {tex} 60 ^ { \circ } {/tex} with the horizontal direction with a velocity of {tex} 150 \mathrm { ms } ^ { - 1 } {/tex}. Then the time after which its inclination with the horizontal is {tex} 45 ^ { \circ } {/tex} is
Question 65 :
Two particles are projected simultaneously from the same point, with the same speed, in the same vertical plane, and at different angles with the horizontal in a uniform gravitational field vertically downwards. A frame of reference is fixed to one particle. The position vector of the other particle, as observed from this frame, is {tex} \vec { r } {/tex}. Which of the following statements is correct?<br>
Question 66 : A particle is ejected from the tube at {tex} A {/tex} with a velocity {tex} v {/tex} at an angle {tex} \theta {/tex} with the vertical {tex} y {/tex} -axis. A strong horizontal wind gives the particle a constant horizontal acceleration a in the {tex} x {/tex} -dircction. If the particle strikes the ground at a point directly under its released position and the downward {tex} y {/tex} -acceleration is taken as {tex} g {/tex} then<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Advanced/5f2beeca36e8973c718889ff"><br>
Question 67 :
A train is moving slowly on a straight track with a constant speed of $2$ $ms^{-1}$. A passenger in that train starts walking at a steady speed of $2$ $ms^{-1}$ to the back of the train in the opposite direction of the motion of the train. So to an observer standing on the platform directly in front of that passenger, the velocity of the passenger appears to be?
Question 68 : An elevator is moving upwards with constant acceleration. The broken curve shows the position {tex} y {/tex} of the ceiling of the elevator as a function of time {tex} t {/tex}. A bolt breaks loose and drops from the ceiling<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Advanced/5e37f74c3df3381b1c314984"><br>Which curve best represents the position of the bolt as a function of time?
Question 69 :
A tube of length {tex} L {/tex} is filled completely with an incompressible liquid of mass {tex} M {/tex} and closed at both the ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity {tex} \omega {/tex}. The force exerted by the liquid at the other end is<br>
Question 70 :
The speed of a projectile at its highest point is {tex} v _ { 1 } {/tex} and at the point half the maximum height is {tex} v _ { 2 } . {/tex} If {tex} \frac { v _ { 1 } } { v _ { 2 } } = \sqrt { \frac { 2 } { 5 }}{/tex} then find the angle of projection
Question 71 : The acceleration of a particle starting from rest and travelling along a straight line is shown in the Fig. The maximum speed of the particle is<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Advanced/5e37f4ff3df3381b1c3148cb"><br>
Question 72 :
A truck is moving with a constant velocity of {tex} 54 \mathrm { kmh } ^ { - 1 } {/tex}. In which direction (angle with the direction of motion of truck) should a stone be projected up with a velocity of {tex} 20 \mathrm { ms } ^ { - 1 } , {/tex} from the floor of the truck, as to appear at right angles to the truck, for a person standing on earth?<br>
Question 73 :
Two boys {tex} P {/tex} and {tex} Q {/tex} are playing on a river bank. {tex} P {/tex} plans to swim across the river directly and come back. {tex} Q {/tex} plans to swim downstream by a length equal to the width of the river and then come back. Both of them<br>bet each other, claiming that the boy succeeding in less time will win. Assuming the swimming rate of both {tex} P {/tex} and {tex} Q {/tex} to the same, it can be concluded that<br>
Question 74 :
A stone tied to a string of length {tex} L {/tex} is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position and has speed {tex} u {/tex}. The magnitude of the change in its velocity as it reaches a position where the string is horizontal is
Question 75 : In Fig, the angle of inclination of the inclined plane is {tex} 30 ^ { \circ } . {/tex} Find the horizontal velocity {tex} V _ { 0 } {/tex} so that the particle hits the inclined plane perpendicularly<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Advanced/5e37f4903df3381b1c3148a7"><br>
