 Ghargay, Assistant Professor, Department of Civil Engineering from WIT, Solarpur. Topic for today's session is relative velocity and learning outcome of this session. At the end of this session, learner will be able to determine the relative velocity of moving body with respect to other moving body. Let us see diagrammatically. Here there is a vehicle A moving with a velocity 60 kilometer per hour. On the parallel track vehicle B is there moving with the same velocity 60 kilometer per hour. As the velocity of both the vehicle is same, so after time t they will reach at a same position and the observer in a vehicle A will think that B is not moving or it is at a rest position. Same here observer in a B will think that car A is not moving, it is at a same position. So according to the observer relative velocity of both the car is 0. So here the difference between velocity and the relative velocity is that when we are talking about velocity only in that observer is a stationary and when we are talking about the relative velocity in that observer is also having some velocity. Now in second case, increase the speed of car B, keep it little faster than the car A. So let speed of car A is 60 kilometer per hour and the velocity of car B is 70 kilometer per hour. So after time t, the car B will cover some distance more than the car A. So the observer in car A will think that car B is moving with a very slow speed that is 10 kilometer per hour and the observer in a car B will think that the car A is moving in a reverse direction. So according to B, the velocity of A is minus 10 kilometer per hour and according to A, the velocity of B is 10 kilometer per hour. Now we will discuss the motion on parallel path in opposite direction. Here car A and car B are moving parallely but in opposite direction. Say the velocity of car A is 60 kilometer per hour and velocity of car B is 30 kilometer per hour. When the there is two car will pass each other at the time interval t, they feel that the opposite car is moving very fast. So according to the observer in a car A, the relative velocity of car B is 90 kilometer per hour. Same according to B, the velocity of car A is 90 kilometer per hour. So here there is a addition of two velocity. Now we will discuss now the motion in a plane in any direction but in a one plane. Now we will only consider the direction of velocity and find out the component of velocity in x direction and the y direction. So how we resolve the force? Similar way you resolve the velocity and find out the velocity component in x direction and the y direction. Now we will first find out the velocity of A with respect to B. So first find out the relative velocity component in x direction. In x direction there are two components VAX and VBX. So VAX and VBX both the velocity component are moving in a same direction. So the relative velocity is the subtraction of these two velocity because we have seen the same case in a motion in a parallel track in like direction. In y direction there are two velocity components VAY and VBY. They are exactly acting opposite to each other. So there is the addition of these two components VAY plus VBY. It is the relative velocity component in y direction. So the relative velocity is under root of VRX square plus VRY square. Same way the velocity of B with respect to A is also under root of VRX square plus VRY square but here VRX or VRY value may different. Now you pause the video here think and answer the question. For the calculation of relative velocity of B with respect to A what will be the relative velocity component in x and y direction? So this is your figure. You refer the figure and calculate the relative velocity component in x and y direction. We will see one by one. In option A it is given that VRX is equal to VAX minus VBX. It is a relative velocity of A with respect to B but in question it is asked that we have to find out B with respect to A. So this is not a correct option. So VRX is equal to VBX minus VX. It is a correct option and VRY is equal to VAY plus VBY. So here y components are opposite in direction. So there must be an addition of this component. So this is also correct. So both VRX and VRY shown correct in option B. So B is correct option. We will see third option also. VRX is equal to VAX plus VBX. So this is how we calculate the resultant. When the forces are acting in same direction we generally do the addition. So for the calculation of resultant we follow the calculation as per the option C and vertical components are exactly opposite in direction. So there is a subtraction but it is not a resultant force calculation. Now we will solve one numerical here. In the numerical the two vehicles are moving from the same point at the same time with the velocity VA is given 30 kilometer per hour and VB is given 40 kilometer per hour and inclination with Y direction is given 30 degree and 45 degree. So two vehicles move from same point at the same time as shown in figure, determine the relative velocity of A with respect to B and the distance between them after half an hour. So we will find the solution. So here two velocities are there in any direction. So we know that we have to find out the component of that velocity in X and Y direction and inclination is given 30 degree with vertical. So vertical component will be 30 cos 30 and horizontal component will be 30 sin 30. Similarly find out the horizontal and vertical component for the VB for that angle is given 45 degree with vertical. So vertical component will be 40 cos 45 and horizontal component will be 40 sin 45. Now we will continue with the same figure. We have to determine the relative velocity of A with respect to B. So first calculate relative velocity component in X direction. So see here in X direction there are two velocities VBX and VAX. So here we have to determine velocity of A with respect to B. So VAX minus VBX this will be our formula. So 30 sin 30 minus 40 sin 45 it will give you minus 13.284 kilometer per hour. So it is obviously if you calculate 40 sin 45 it is approximate 28.28 kilometer per hour and if you check the 30 sin 30 it is 15 kilometer per hour. So velocity of B is more as compared to velocity of A. According to B it must be in a reverse direction. So it is minus 13.284 kilometer per hour. Now calculate relative velocity component in Y direction. In Y direction there are two velocities 30 cos 30 and 40 cos 45. They are in exactly opposite direction. So we have to do this addition of this two velocity. It is 54.265 kilometer per hour. Now put VRX and VRY in the formula of relative velocity. It is under root of VRX square plus VRY square similar to resultant formula. Calculate relative velocity of A with respect to B. It will be 55.867 kilometer per hour. Now draw the vector diagram. So VRX is minus 13.284 means it is moving in reverse direction. So in vector diagram we have to show the direction also. And with respect to B vehicle A is moving in opposite direction. So this with the opposite direction with respect to B that is 54.264. So it is vertical component and this is the horizontal component. And the resultant velocity of A is 55.86 kilometer per hour. So this is called as the relative velocity of A with respect to B. Similarly vector diagram of relative velocity of B with respect to A also you can draw here. All the calculation will be same. Only the change will be that. You will get VRX is plus 13.284. So plus 13.4 means in the direction of velocity. So this is the direction of the velocity in x direction. And with respect to A B is moving in opposite direction. So this is the vertical direction of velocity. And as per the vector diagram we join the first point and second point. And from first point to second point will indicate the direction of the relative velocity. So this will be the vector diagram for the relative velocity of B car with respect to A. In the same question there is one more question find the relative distance of vehicle A with respect to B after half an hour. And it is very simple that the distance is equal to velocity into time. So we have calculated the relative velocity that is 55.867 kilometer per hour and time is given half an hour. So you will get the relative distance of A with respect to B is 27.933 kilometer. These are my references. Thank you very much.