Kinematics Questions and Answers

3 Problem 5 An arrow is shot from a height of 1 6 m toward a cliff of height H It is shot with a velocity of 35 m s at an angle o move the horizontal It lands on the top edge of the cliff 3 91 s later

A particle is moving along the x axis with its coordinate with the time t given be x t 10 8t 3t Another particle is moving the y axis with its coordinate as a function of time given by y t 5 8t At t 1s the speed of the second particle as measured in the frame of the first particle is given as v Then v

In the figure shown p is a point in x y plane whose position vector is r f and are unit vectors along r and perpendicular to r respectively in x y plane as shown d d d f d d de 20 de 20 d X de de de de Then fx X Y rx X

3 A particle is executing SHM along a straight line Its velocities at distances x and x2 from the mean are v and v2 respectively Its time period is CBSE AIPMT 2015 EAMCET 2013 position a 2 c 2 2 x x 2 22 2 v 2 V v 2 2 2 x x x2 b 2 x 2 x V0 0 20 V d 2 2 10 0 2 V x x 2

Paragraph for Questions 9 and 10 In a square field of size 20m there are two coconut trees A B at diagonally opposite corners of height 40 m and 20m respectively A bird comes flying over the top of tree A along a straight line towards top of tree B with a constant speed of 10 3 m s Same time after the bird passes the top of tree A a water 1 jet is fired vertically from the centre of the field which strikes the bird after s of firing Find the distance of bird from the top of taller tree when jet was fired A 5 3 m B 10 3 m C 5 2 m How high above the smaller coconut tree the bird is hit by the jet A 5 3 m B 10 m C 5 2 m D None of these D None of these

A helicopter blade spins at exactly ins Its tip is 5 00 m from the center of rotation Calculate the average speed and average velocity 1 s with respect to the ground 2 of the blade tip in in ms 1 5 10 2 B revolution 2 5 7 5 2 LC

An elevator of height 6 m starts from rest and moves upwards with constant acceleration of 2 m s2 After 20 s from start a bolt from the ceiling of elevator detaches and then hits the floor of elevator If the distance travelled by bolt till the time S it hits the floor in metres is S then find g 10 m s

39 7 Five forces F F F3 F and F are acting on a particle of mass 2 kg so that it is moving with 4 m s in east direction If force Fis removed then the acceleration becomes 7 m s in north then the acceleration of the block if only F is acting will be

A uniform rod of length 200 cm and mass 500 g is balanced on a wedge placed at 40 cm mark A mass of 2 kg is suspended from the rod at 20 cm and another unknown mass m is suspended from the rod at 160 cm mark as shown in the figure Find the value of m such that the rod is in equilibrium g 10 m s 0 20 cm 40 cm 2 kg 160 cm m

Q 21 A wet open umbrella is held upright and is rotated about the handle at a uniform rate of 21 revolutions in 44 s If the rim of the umbrella is circle of 1 metre in diameter and the height of the rim above the floor is 1 5 m the drops of water spun off the rim and hit the floor at a horizontal m from umbrella Josido gril

A small block of mass m placed over a wedge of mass M The block is pushed on the wedg at a speed v Assume that all the surfaces are frictionless initial velocity of block is horizonta Wedge has gradual curvature Vy Vx M M m a Find the speed of the smaller mass when it breaks off the larger mass at height h b Find the maximum height from the ground that smaller mess

We know how by neglecting the air resistance the problems of projectile motion can be easily solved and analysed Now we consider the case of the collision of a ball with a wall In this case the problem of collision can be simplified by considering the case of elastic collision only When a ball collides with a wall we can divide its velocity into two components one perpendicular to the wall and other parallel to the wall If the collision is elastic then the perpendicular component of velocity of the ball gets reversed with the same magnitude Vcose Vcose 0 i Velocity just before collision Vsine Vsine Components of velocity Components of velocity just before collision just after collision The other parallel component of velocity will remain constant if given wall is smooth Now let us take a problem Three balls A and B C are projected from ground with same speed at same angle with the horizontal The balls A B and C collide with the wall during their flight in air and all three collide perpendicularly with the wall as shown in figure 18 Which of the following relation about the maximum height H of the three balls from the ground during their motion in air is correct 1 HA Hc HB 2 HA HB Hc 3 HA HC HB 4 HA HB Hc

51 From the top of a 11 m high tower a stone is projected with speed 10 m s at an angle of 37 as shown in figure Find a time of flight b horizontal range c speed just before striking the ground Ans a 1 s b 8 m c 8 5 m s f X 11 m www 10 m s

t 3 1 39 A launch travels across a river from a point A to a point B on the opposite bank along the straight line AB forming an angle a with the bank as shown in figure 1 160 The flag on the mast of the launch makes an angle with its direction of motion Determine the speed of the launch with respect to the bank Let u be the velocity of wind blowing in the direction perpendicular to the current A B J a Figure 1 160 B U

First write down the symbolic equation for the vertical distance y as a function of time t then derive the algebraic form for calculating t in terms of y and voy launcher is 20cm off the ground shooting at a 20degree angle

Every once in a while a bird will get hit by a baseball during a baseball game The on longest home runs in baseball land about 500 0 feet which is 152 4 meters from home plate If these balls leave the bat at a 45 0 degree angle to maximize their distance what is the safe height in meters for birds around baseball stadiums isrit herlich s269 Vove

A radioactive isotope X has a half life of 10 s There are 1000 isotopes which are falling from rest from a height of 500 m When it is at a height of 100 m from the reference plane find the activity of the sample 1 50 3 29 2 39 4 100

A rabbit is hidden in grass at a point A near a pond A dog is drinking water at a point B in the pond The rabbit can run on the ground with a velocity 31 4 ms Dog can run with a speed 89 ms The coordinate of points B and A are 0 0 and 5 10 respectively If the rabbit starts to run immediately the dog starts then dog catches rabbit in minimum time to Tick the correct alternative s A X component of velocity of dog will be 5 ms B Y component of velocity of dog will be 8 ms 5 C The value of to will be s 2 D Data insufficient

body of mass 150 gm is dropped from point A takes time t seconds to reach the point B at the ground Once more the same ody is dropped from point A and when body traverses half the distance a bullet of mass 50gm moving horizontally with speec 0 m s hits the falling body at point C and sticks to it The total time of flight of the body in this case is t2 seconds and body strikes he ground at point D The air drag should be neglected Take g 10 m s2 Then find the ratio of t t2 A M H 160 m m 40 m s C B

In the system is shown a 10 kg horizontal cylinder suspended from string from the ceiling and supported by two fixed frictionless slopes A and B If normal reaction applied by slope A on the cylinder is 30 N which of the following conclusion can you make g 10 m s A HO 53 37 B A No tension force is applied by the string on the cylinder B Tension force applied by the string on the cylinder is 50 N C Normal reaction applied by the slope B on the cylinder is 60 N D Normal reaction applied by the slope B on the cylinder is 40 N

Objective Solve problems for projectiles launched horizontally and at various angles to the horizontal to calculate maximum height range and overall time of flight of the projectile Procedure Complete the table below A football player kicked the ball at a speed of 27 0 m s as shown in the figure Determine the range and the height achieved by the ball at a given angle Assume that the speeds are the same at a different angle Angle 20 35 45 55 70 Time of flight 3 2 s 6 2 S 5 2 s Hieght 4 4 m 18 6 m Range 71 m

A swimmer can swim in still water with a speed of 5 m s While crossing a river his speed is 3 m s with respect to ground If he crosses the river in the shortest possible time what is the speed of flow of water in m s

A particle has initial velocity 21 6 m s The particle experiences a const 1 2 ms The velocity of particle becomes parallel to x axis at tequal to 2 s 3 s 4 s 6 s Solution Answer 2 v t 21 6 i 2j t tv 6 2t j

10 A person crosses a river along the path AB and again returns to A through same path BA River flows with speed up and the person s speed with respect to water is v constant If the path AB makes an angle 0 with the river flow then find the ratio of time to cross the river from A to B and to return to A from B to A v Uo A 50 B U

A ball is thrown from a point on ground and it lands on same level at distance of 240 m and its time of flight is 8 sec The initial velocity in m s of projection is 10a then a is

The current velocity of a river is directly proportional to the perpendicular distance from its bank and is its maximum vo in the middle Near the banks the velocity is zero A boat is moving in the river such that its velocity u relative to the river flow is constant and perpendicular The horizontal drift through which the boat crossing the river will be carried away by the A VOC 2u current The horizontal drift through which the boat crossing the river will be carried away by the B Voc 4u current CIU C Time taken by the boat to cross the river will be D Time taken by the boat to cross the river will be 211

A block of m 10 kg is kept on ground A vertically upward force F 10 t N where t is the time in seconds starts acting on it at t 0 as shown in figure F 10t 10kg A Time at which block loose contact from the surface is 10 sec B Velocity of block at t 20 sec is 50 m s C Velocity of block at t 20 sec is 200 m s 500 D Displacement of block in 20 sec is 3 m

average speed of traffic advancement i s 5 m s when green and red lights rem ain open for same duration To avoid tr affic jam at peak hour duration of openi ng green light is doubled keeping durati on same what is the new speed of traf fic advancement in m s

Position x of a particle moving along the x axis varies with time t according to equation x t 1 31 8t 10 where x is in meters and t is in seconds A student records velocity and acceleration of the particle at different instants of time and reports his readings Some of those readings are given below Which of them is are correct A At instant t 1s velocity is 3 m s and acceleration is 4 m s B At instant t 2s velocity is 0 m s and acceleration is 2 m s C At instant t 3s velocity is 1 m s and acceleration is 0 m s D At instant t 4s velocity is 0 m s and acceleration is 2 m s

Two stones A and B are projected simultaneously as shown in figure It has been observed that both the stones reach the ground at the same place after 7 sec of their projection Determine difference in their vertical components of initial velocities in m s g 9 8 m s 49m

A man jumps from a stationary helicopter which is situated at a height of 100 m If the man opens the parachute after falling a distance 80 m and finally reaches the ground at 10 m s If net retardation by 2a parachate is a in m s find 25 gonnon finn pro choum in figura The dashed ling shown th inatom in th nga of

A projectile is projected on the inclined plane as shown V V are components of it s initial velocity along the incline and perpendicular to incline and V V4 are components of it s final velocity along the incline and perpendicular to incline Here we are comparing the magnitudes only A V V3 B V V3 10 V V C V V D V V4

A cart has mass 2 metric tone and sand of 1 metric tone is inside the cart Now a force of 10 N is applied on cart and sand starts to leak with rate of 0 5 kg s What is the velocity of cart when total sand has come out from the cart a 13 86 m s 1 F 10 N b 0 06 m s

A thin but rigid semicircular wire frame of radius r is hinged at and can rotate in its own vertical plane A smooth peg P starts from O and moves horizontally with constant speed vo lifting the frame upward as shown in figure wollis et trigi Item 0 60 P Vo Find the angular velocity of the frame when its diameter makes an angle of 60 with the vertical a v r b vo 2r c 2v r d vor

Q 97 A stone is thrown from the ground towards a wal 6m high at a distance of 4m such that it just clear the top of the wall at its highest point Find the speed and angle of projection of the stone Sol

A solia spherical ball of mass 0 5 kg and radius 10 cm rolls to the top or a nili as snown in figure Kinetic energy of the ball at the bottom of hill is 140 J As the ball moves up the hill it rolls without slipping Height of the hill is 16 m As the ball reaches the top of the hill it is moving horizontally From the top of hill it will move into air and fall freely under gravity Assuming that no work is done against friction as the ball rolls and neglecting air resistance g 10 m s KE 140J A 16m B C at of th bill

A body is projected into air in such away that maximum reached by it is horizontal range It g 10m s and horizontal range is 80 3 m Column 1 Column II A Time of flight B Angle of projection in degrees C Velocity of projection in m sec D Acceleration of projectile in m sec P 40 Q 4 3 R 10 S 60

lulum of mass m is attached to a block of mass M The block slides on a horizontal frictionless surface Find the Lagrangian and equation of motion of the pendulum For small amplitude oscillations derive an expression for periodic time X X

A batsman hits a sixer and the ball touches the ground outside the cricket field Which of the following graph describes the variation of the cricket ball s vertical velocity v with time between the time t as it hits the bat and time 12 when it touches the ground e 2 3 14x Velocity Velocity Velocity Velocity t

At t 0 a train approaching a station begins decelerating from a speed of 160 mi hr according to the acceleration function a t 1280 1 4t 3 mi hr where t 0 How far does the train travel between t 0 and t 0 2 Between t 0 2 and Between t 0 and t 0 2 the train travelsmi Round to three decimal places as needed Between t 0 2 and t 0 5 the train travels mi Round to three decimal places as needed

AIIMS 5 pt tve C 2 n ve O VA 3 Displacement area under graph Acceleration tane Increasing 0 Increases JV 0 90 t Frenca it nec inces ve Decre VA Diss Ace ve Det VA Motion in a Straight Line 43 pisi ve JUA 0 Decreases Ane t stru Acceleration tane Positive decreasing Displacement area under graph ove Dec CAMERA 8 90 Increa

1 68 A particle where t in s gives v in m s The v 2 t 1 particle starts from origin Find the y cordinate when the x coordinate becomes zero after start 2 3 8 5 m 24 3 4 3 E m locity

The path of projectile is represented by Y Ax Bx A A The range of the projectile is given by B B The range of the projectile is given by 4A B A C The maximum height reached by it is given by 4B2 D The maximum height reached by it is given by m sec

2 16 A boat crosses a river from port A to port B which are just on the opposite side The speed of the water is Vw and that of boat is VB relative to still water Assume VB 2Vw What is the time taken by the boat if It has to cross the river directly on the AB line 3D 2V B 2D a VB 3 b c D VBVZ d D 2 VB

Q 19 A particle starts from rest and experiences constant acceleration for 6 s if it travels a distance d in the first two second a distance d in the next two seconds and a distance de in the last two second then a d d d3 1 1 1 c d d d3 1 3 5 b d d d d d d3 1 2 3 d3 1 5 9

Q 21 A small block sides without friction down an inclined plane starting from rest Let S be the distance travelled from time t n 1 tot n Then Sn is Sn 1 b a 2n 1 2n 2n 1 2n 1 C 2n 1 2n 1 2n 2n 1 d

A small particle is attached to an inextensible string and placed on a table The other end is pulled with constant acceleration towards right Initially the particle was at rest After the particle leaves the edge of table the maximum vertical displacement of the particle ism Find the length of string in m m

Question A boy standing at the top of a tower of 20m height drops a stone Assuming g 10 ms 2 the velocity with which it hits the ground is O O O 20 0 m s 40 0 m s 5 0 m s 10 0 m s

A rod of mass m length is moving between perpendicular smooth walls as shown When the rod is at an angle with horizontal its end A is moving right with speed v The speed of end B is 1 v cot 2 v tan 3 v cos 0 4 v sin YA B A X Page

Q 24 From the top of tower a stone is thrown up It reaches the ground in t second A second stone thrown down with the same speed reaches the ground in t second A third stone released from rest reaches the ground in t3 second Then b t3 t t d t t t a t3 1 c t3 t t 2 1 t 1 t