Question 1 :
Two boys are standing at the ends {tex} A {/tex} and {tex} B {/tex} of a ground where {tex} A B = a {/tex} . The boy at {tex} B {/tex} starts running in a direction perpendicular to {tex} A B {/tex} with velocity {tex} v _ { 1 } {/tex} . The boy at {tex} A {/tex} starts running simultaneously with velocity {tex} v {/tex} and catches the other boy in a time {tex} t , {/tex} where {tex} t {/tex} is

Question 2 :
The position vectors of points {tex} \mathrm { A } , \mathrm { B } , \mathrm { C } {/tex} and {tex} \mathrm { D } {/tex} are {tex} \mathrm { A } = 3 \hat { \mathrm { i } } + 4 \hat { \mathrm { j } } + 5 \hat { \mathrm { k } } , \mathrm { B } = 4 \hat { \mathrm { i } } + 5 \hat { \mathrm { j } } + 6 \hat { \mathrm { k } } , \mathrm { C } = 7 \hat { \mathrm { i } } + 9 \hat { \mathrm { j } } + 3 \hat { \mathrm { k } } {/tex} and {tex} \mathrm { D } = 4 \hat { \mathrm { i } } + 6 \hat { \mathrm { j } } {/tex} then the displacement vectors {tex} \overline { \mathrm { AB } } {/tex} and {tex} \overline { \mathrm { CD } } {/tex} are

Question 3 :
A car runs at a constant speed on a circular track of radius {tex} 100 \mathrm { m } , {/tex} taking 62.8 seconds in every circular loop. The average velocity and average speed for each circular loop respectively, is

Question 4 :
A particle is projected with a velocity {tex} v {/tex} such that its range on the horizontal plane is twice the greatest height attained by it. The range of the projectile is (where {tex} g {/tex} is acceleration due to gravity)

Question 5 :
A bullet is fired with a speed of {tex} 1500 \mathrm { m } / \mathrm { s } {/tex} in order to hit a target {tex} 100 \mathrm { m } {/tex} away. If {tex} \mathrm { g } = 10 \mathrm { m } / \mathrm { s } ^ { 2 } . {/tex} The gun should be aimed

Question 6 :
Two pegs {tex} A {/tex} and {tex} B {/tex} thrown with speeds in the ratio {tex}1: 3{/tex} acquired the same heights. If {tex} A {/tex} is thrown at an angle of {tex} 30 ^ { \circ } {/tex} with the horizontal, the angle of projection of {tex} B {/tex} will be

Question 7 :
The velocity of projection of oblique projectile is {tex} ( 6 \hat { \mathrm { i } } + 8 \hat { \mathrm { j } } ) \mathrm { ms } ^ { - 1 } {/tex} . The horizontal range of the projectile is

Question 8 :
A particle is projected with some angle from the surface of the planet. The motion of the particle is described by the equation; {tex} x = t , y = t - t ^ { 2 } {/tex}. Then match the following columns:<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NEET/5df31d368701466b65e04dd8"><br>

Question 9 :
A ball rolls off to the top of a staircase with a horizontal velocity {tex} \mathrm { u } \ \mathrm { m } / \mathrm { s } {/tex}. If the steps are {tex}h{/tex} metre high and {tex}b{/tex} metre wide, the ball will hit the edge of the {tex} \mathrm n^{th}{/tex} step, if

Question 10 :
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} 147 \mathrm { ms } ^ { - 1 } {/tex}. Then the time after which its inclination with the horizontal is {tex} 45 ^ { \circ } , {/tex} is

Question 11 :
{tex}\mathbf {Assertion} {/tex} : The horizontal range is same when the angle of projection is greater than {tex} 45 ^ { \circ } {/tex} by certain value and less than {tex} 45 ^ { \circ } {/tex} by the same value.<br>{tex}\mathbf {Reason} {/tex} : If {tex} \theta = 45 ^ { \circ } + \alpha {/tex}, then {tex} R _ { 1 } = \frac { u ^ { 2 } \sin 2 \left( 45 ^ { \circ } + \alpha \right) } { g } = \frac { u ^ { 2 } \cos 2 \alpha } { g }{/tex} .<br>If {tex} \theta = 45 ^ { \circ } - \alpha , {/tex} then {tex} R _ { 2 } = \frac { u ^ { 2 } \sin 2 \left( 45 ^ { \circ } - \alpha \right) } { g } = \frac { u ^ { 2 } \cos 2 \alpha } { g } {/tex}<br>

Question 12 :
A ball is thrown at an angle {tex} 75 ^ { \circ } {/tex} with the horizontal at a speed of {tex} 20 \mathrm { m } / \mathrm { s } {/tex} towards a high wall at a distance d. If the ball strikes the wall, its horizontal velocity component reverses the direction without change in magnitude and the vertical velocity component remains same. Ball stops after hitting the ground. Match the statement of {tex}\mathrm{ Column\ I}{/tex} with the distance of the wall from the point of throw in {tex}\mathrm{ Column\ II}{/tex}<br><br><table> <tr><th>Column I </th> <th>Column II</th> </tr> <tr><td>(A)Ball strikes the wall directly </td> <td>(1)8m</td> </tr> <tr><td>(B)Ball strikes the ground at x=12m from the wall</td> <td>(2)10m</td> </tr> <tr><td>(C)Ball strikes the ground at x=10m from the wall</td> <td>(3)0m</td> </tr> <tr><td>(D)Ball strikes the ground at x=5m from the wall</td> <td>(4)25m</td> </tr> </table>

Question 13 :
Two identical particles are projected horizontally in opposite directions with a speed of {tex} 5 \mathrm { ms } ^ { - 1 } {/tex} each from the top of a tall tower as shown. Assuming {tex} \mathrm { g } = 10 \mathrm { ms } ^ { - 2 } {/tex}, the distance between them at the moment when their velocity vectors become mutually perpendicular is<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NEET/5e0dc675e50f934b847a5a64"><br>

Question 14 :
If retardation produced by air resistance of projectile is one-tenth of acceleration due to gravity, the time to reach maximum height

Question 15 :
A projectile of mass {tex} \mathrm { m } {/tex} is thrown with a velocity v making an angle {tex} 60 ^ { \circ } {/tex} with the horizontal. Neglecting air resistance, the change in velocity from the departure A to its arrival at B, along the vertical direction is<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NEET/5e0dc58de50f934b847a59a3">

Question 16 :
If {tex} \overrightarrow { \mathrm { A } } = \hat { \mathrm { i } } + \hat { \mathrm { j } } + \hat { \mathrm { k } } {/tex} and {tex} \overrightarrow { \mathrm { B } } = 2 \hat { \mathrm { i } } - \hat { \mathrm { j } } + 4 \hat { \mathrm { k } } {/tex} then the unit vector along {tex} \overrightarrow { \mathrm { A } } + \overrightarrow { \mathrm { B } } {/tex} is

Question 17 :
For motion in two or three dimensions, the angle between velocity and acceleration is

Question 18 :
If the sum of two unit vectors is a unit vector, then the magnitude of their difference is

Question 19 :
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} 147 \ \mathrm { ms } ^ { - 1 } . {/tex} Then the time after which its inclination with the horizontal is {tex} 45 ^ { \circ } , {/tex} is

Question 20 :
If the angles of projection of a projectile with same initial velocity exceed or fall short of {tex} 45 ^ { \circ } {/tex} by equal amounts, then the ratio of horizontal ranges is

Question 21 :
A particle moves in the {tex} \mathrm { X } - \mathrm { Y } {/tex} plane with a constant acceleration {tex} 1.5 \mathrm { m } / \mathrm { s } ^ { 2 } {/tex} in the direction making an angle of {tex} 37 ^ { \circ } {/tex} with the {tex} \mathrm { X } {/tex} -axis. At {tex} \mathrm t = 0 {/tex} the particle is at the origin and its velocity is {tex} 8.0 \mathrm { m } / \mathrm { s } {/tex} along the {tex} \mathrm { X } {/tex}-axis. Find the position of the particle at {tex} \mathrm t = 4.0 \mathrm { s } {/tex}.