 ##### Introduction

This video introduce us the motion in 2 and 3 Dimensions. We will be considering the object as non deformable

##### Position

In this video we learn about Magnitude ? Angle vector notation and the unit vector notation, and relation between them to define the position of the object in 2 and 3 dimensions.

##### Dist Disp

In this video we will understand the difference between the distance and displacement. And also understand vector representation of displacement in 2 and 3D.

##### Velocity Speed

In this video we learn about average speed and velocity and instantaneous speed and velocity. And representation of velocity in 2 and 3 D.And the graphical meaning of instantaneous velocity.

##### Acceleration

In this video we study about the acceleration representation in 2 and 3 D. And also understand why even speed is constant the acceleration may not be zero. Graphical meaning of acceleration. And vector form of equation of motion for 2 and 3 D considering acceleration constant.

##### Eqs and Graphs

In this video we understand that the motion in each direction is independent to each other and hence one can independently apply equations of motion in each direction.

##### Projectile - I

In this video we understand what is projectile? We will aslo see an example which proves that x and y axis motion are independent to each other. And notations of a projectile motion for which the point of projection and landing are at same level.

##### Projectile - II

In this video we will learn about the derivation of finding the range, maximum height attain, time of flight of a projectile for which the point of projection and landing are at same level. And equation of trajectory.

##### Q1

For a horizontal projectile, figure gives the range R of the ball versus its launch angle qo. Rank the three lettered points on the plot according to
(a) the total flight time of the ball and
(b) the balls speed at maximum height greatest first.

##### Q2

A ball is thrown at an angle of 300 with an initial speed of 30 m/s. Assume that the ball travels in a vertical plane, calculate
a) the time at which the ball reaches the highest point.
b) the maximum height reached.
c) the horizontal range of the ball.
d) the time for which the ball is in the air.
e) other angle for same range.
f) velocity and position of ball at t = 2 sec.

##### Q3

A projectile is projected with initial velocity ( 6 i + 8 j ) m/s. If g = 10 ms-2.Find
a) Horizontal range
b) Time after which its inclination with the horizontal is 45o?

##### Inc Projectile - I

In this video we will first discuss about the change in motion that will occur when we consider motion in incline direction. The meaning of maximum height in case of incline motion. And at last derivation of the range along the incline, maximum height , time of flight and the equation of trajectory considering the motion with respect to the horizontal and vertical direction .

##### Inc Projectile - II

In this video we learn derivation of the range along the incline, maximum height , time of flight and the equation of trajectory considering the motion with respect to the incline direction and the direction perpendicular to the inclined plane.

##### Q4

A particle is projected up an inclined plane of inclination b , at an elevation a to the horizontal. Show that.
a) tan a = cot b + 2tan b , if the particle strickes the plane at right angles.
b) tan a = 2tan b , if the particle strikes the plane horizontally.

##### Rel Motion - I

In this video we understand the meaning of frame of reference, point of reference. And what do we mean by the relative motion? The object is stationary in one frame.
And how the equation of motion can be applied.

##### Rel Motion - II

In this video we will understand how to deal with the relative motion case when the object is moving with the given frame. And a brief of finding the relation between the motion of object in these different frame of references using vector notation.

##### Q5

A boat can travel at a speed 10 m/s in still water. What will be the speed of boat while going:
a) Downstream
b) Upstream
if the river is flowing at 5 m/s.

##### Rel Motion - III

In this video we extended our discussion on finding the relation between the motion in one frame with respect to other frame of reference. And vector representation of these relation.

##### Q6

A small body is dropped from a rising balloon. A person A stands on ground, while another person B is on the balloon. Choose the correct statement: Immediately, after the body is released.
a) A and B, both feel that the body is coming (going) down.
b) A and B, both feel that the body is going up.
c) A feels that the body is coming down, while B feels that the body is going up.
d) A feels that the body is going up, while B feels that the body is going down.

##### Q7

Car A is traveling east at the constant speed of 10 m/s as shown in Figure. As car A crosses the intersection, car B starts from rest 50 m north of the intersection and moves south with a constant acceleration of 2 m/s2. Determine the position, velocity and acceleration of B relative to A, 5 sec after A crosses the intersection.

##### Q8

A person driving a bike is standing on the road on a rainy day. If he starts to move with velocity v, In which direction will the rain appear to him if
a) Rain is falling vertically with speed v
b) Rain is falling at an angle of 45o away from him with speed =

##### Q9

A boy is playing with ball inside a moving vehicle as shown. If acceleration to him is throwing the ball straight up and catching it back. What will be the motion of the ball as seen by an observer on the ground?

##### 1

In figure, a rescue plane files at 180 km/h (= 50.0 m/s) and constant height h = 500 m toward a point directly over a victim, where a rescue capsule is to land. A plane drops a rescue capsule while moving at constant velocity in level fight. While falling, the capsule remains under the plane.
a) What should be the angle of the pilots line of sight to the victim when the capsule release is made ?
b) Velocity of the capsule just before it lands

##### 2

A ball is thrown from the top of a building 45 m high with a speed 20 m/s above the horizontal at an angle of 300. Find
a) The time taken by the ball to reach the ground.
b) The speed of the ball just before it touches the ground.
c) How far is it from the tower when it lands. Take g = 10 m/s2

##### 3

Two balls are thrown with the same initial velocity at angles q and (90 - q) with the horizontal. Find the ratio and sum of the maximum heights attained by them.

##### 4

Projectile motion of an object is shown in the figure. The angle that its instantaneous velocity makes with the horizontal is given as a function of time.
The ball lands at t = 6.0 s.
a) What is the magnitude vo of the launch velocity.
b) At what height above the launch does the ball land
c) Direction of travel just as the ball lands

##### 5

A golf ball is struck at ground level. The speed of the golf ball as a function of the time is shown in figure, where t = 0 at the instant the ball is struck.
(a) How far does the golf ball travel horizontally before returning to ground level?
(b) What is the maximum height above ground level attained by the ball?

##### 6

A ball is thrown from a height of 1m above the ground with a velocity of 10 2 m/s with an angle of 45o with the horizontal. There is a wall at a distance of 5m from the point of projection such that the ball rebounds elastically from the wall. Where does the ball hit the ground?

##### 7

From a point on the ground at a distance a from the foot of a pole, a ball is thrown, at an angle of 45o, which just touches the top of pole and strikes the ground at a distance of b, on the other side of it. Find the height of the pole.

##### 8

A particle is projected over a triangle from one extremity of its horizontal base. Grazing over the vertex, it falls on the other extremity of the base. If a and b be the base angles of the triangle and q the angle of projection, prove that
tan q = tan a + tan b.

##### 9

The horizontal range and maximum height attained by a projectile are R and H, respectively. If a constant horizontal acceleration ax = hg is imparted to the projectile due to wind. Find its horizontal range and maximum height.

##### 10

The ratio of the distance carried away by the water current, downstream, in crossing a river, by a boat making same angle with downstream and upstream are, respectively, as 2:1. The ratio of speed of boat to the water current cannot to be less than
(a) 1/3
(b) 4/5
(c) 1/5
(d) 4/3

##### 11

A particle is projected at angle q with the horizontal. Calculate the time when it is moving perpendicular to initial direction. Also calculate the velocity at this position.

##### 12

Car A moves with a velocity of 15 m/s and B with a velocity of 20 m/s as shown figure. Find
(a) relative velocity of B w.r.t. A
(b) relative velocity of A w.r.t. B
(c) if initially they were 10m apart. What is the distance between them after 10 sec.

##### 13

Two roads intersect at right angle, one goes along x-axis and the other along y-axis. At any instant two cars A and B are moving along y and x direction.
Draw the direction of motion of
1. Car A as seen from car B, and
2. Car B as seen from car A.

##### 14

A motorboat going downstream overcame a box at a point A. After time T it turned back and after some time pased the box at a distance l from the point A. Find the flow velocity assuming the duty of the engine to be constant.

##### 15

A river is flowing with velocity vr. A boat, which can move with velocity vb in still water, has to cross the river. In which direction should the boat move, so that it crosses the river
a) in shortest time
b) along shortest path

##### 16

Two swimmers leave point A on one bank of river to reach point B lying right across on the other bank. One of them crosses the river along the straight line AB while the other swims at right angles to the stream and then walks the distance that he has been carried away by the stream to get point B. What was the velocity vw of his walking if both swimmers reached the destination simultaneously? Given the stream velocity is vo and the velocity of each swimmer with respect to water is vs.

##### 17

A boat is moving directly away from a cannon on the shore with a speed v1. The cannon fires a shell with a speed v2 at an angle a and the shell hits the boat. Then
(a) the shell hits the boat when the time equals to (2v2 sin a)/g is lapsed.
(b) the boat travels a distance (2v1v2 sin a)/g from its original position
(c) the distance of the boat from the cannon at the instant the shell is fired is 2(v2 sin a)(v2 cos a - v1)/g
(d) the distance of the boat from the cannon when the shell hits the boat is 2(v2 sin a)(v2 cos a )/g

##### 18

Two shells are fired from a cannon successively with speed u each at angles of projection a and b respectively. If the time interval between the firing of shells is dt and they collide in mid-air after a time t from the firing of the first shell.

##### 19

A ball rolls off the top of a staircase with a horizontal velocity u m/s. If the steps are h meters high and b meters wide, which stair will the ball hit?

##### 20

A stone is projected from the point on the ground in such a direction so as to hit a bird on the top of a telegraph post of height h and then attain the maximum height 3h/2 above the ground. If at the instant of projection the bird were to fly away horizontally with uniform speed, find the ratio between horizontal velocities of the bird and stone if the stone still hits the bird while descending.

##### 21

Two parallel straight lines are inclined to the horizontal at an angle a. A particle is projected from a point mid way between them so as to graze one of the lines and strike the other at the right angle. show that if q is the angle between the direction of projection and either of the lines, then tan q = ( 2 - 1) cot a.

##### 22

Two particles move with constant velocities v1 and v2. At the initial moment their position vectors are equal to r1 and r2.
How must these four vectors be interrelated for the particles to collide?

##### 23

On a frictionless horizontal surface, assumed to be the x-y plane, a small trolley A is moving along a straight line parallel to the y axis with a constant velocity of ( 3 - 1) m/s. At a particular instant, when the line OA makes an angle of 450 with the x axis, a ball is thrown along the surface from the origin O. Its velocity makes an angle f with the x axis and it hits the trolley.
a) The motion of the ball is observed from the frame of the trolley. Calculate the angle q made by the velocity vector of the ball with the x axis in this frame.
b) Find the speed of the ball with respect to the surface, if f = 600

##### 24

Two particles start moving simultaneously with constant velocities u1 and u2 as shown in figure. First particle starts from N along NO and second starts from O along OM. Find the shortest distance between them during their motion.

##### 25

Two particle start simultaneously from the same point and move along two straight lines, one with uniform velocity v and other with a uniform acceleration a. If a is the angle between the lines of motion of two particles then
(a) time at which the relative velocity is least
(b) the least value of relative velocity will be

##### 26

The path of one projectile as seen by an observer on an other projectile is a/an.
(a) straight line
(b) parabola
(c) ellipse
(d) circle

##### 27

Two towers AB and CD are situated at a distance d apart. AB is 20 m high and CD is 30 m high from the ground. An object is thrown from the top of AB horizontally with a velocity of 10 m/s towards CD. Simultaneously another object is thrown from the top of CD at an angle 600 to the horizontal towards AB with the same magnitude of initial velocity as that of the first object. The two objects move in the same vertical plane and collide in mid air. Calculate the distance d between the towers.

##### 28

Two particles A and B are projected from two high rise buildings simultaneously as shown in figure. Find minimum distance between these two particles.

##### 29

Three particles A, B and C are situated at the vertices of an equilateral triangle ABC of side d at t = 0. Each of the particles moves with constant speed v.
A always has its velocity along AB, B along BC and C along CA. At what time will the particles meet each other ?

##### 30

A swimmer has velocity v in still water which is less than the velocity u of the river. Show that the swimmer must aim himself at an angle cos-1 (v/u) with upstream in order to cross the river along the shortest possible path.

##### 31

Find maximum value of range on an incline of angle a with horizontal.

##### 32

For a horizontal projectile with initial velocity u what can be the maximum height reached for a given horizontal distance

##### 33

A stone is being thrown at a speed of u m/s from the top of a h m high building. Find out how far from the foot of the building can the stone be thrown.