Relative motion concept analysis
Today our topic is very interesting and important it is all about relative motion we have study in previous post about motion now be ready for relative motion concept and lets start.
we have study in motion topic if any body is not changing its position with respect to its surrounding then body is called at rest suppose you are holding a tray and on tray one plate with food and one glass with water and going to sit on your dining table now see here plate and glass are at rest with respect to tray while you are moving towards dining table why rest ? because distance between plate, glass are not changing but plate and glass are in motion with respect to dining table because when you are moving distance between plate, glass and dining table are changing. Important concept nothing in the universe is at absolute rest and same nothing is in absolute motion all are relative motion. Hence we need to study relative motion. same body can be at rest and same can be in motion relative to different body. This is called relative motion.
I hope you have got the concept of relative motion.
We know that earth is moving its means every object on the earth is moving then why we say object on the earth is at rest because we say with respect to surface of the earth suppose you are standing at a place the distance of earth surface now and after one minute is same the surface distance is not changing hence you are at rest while earth is moving. so any body at rest or in motion it is relative so we have to understand motion relative to which and at rest relative to which suppose two person are sitting in a moving train in front of each other and no any one is moving then first person is at rest relative to second person because distance between them from any point is not changing similarly second person is at rest with respect to first then train crosses from a platform and a third person is standing at platform seen both of them sitting in train are moving and crosses him so with respect to third person both are moving hence every motion is a relative motion. relative motion is always between two body one is mover and other is observer not only relative word in motion you are also relative how you are son of relative to your father, 20 kg mass is heavy relative to 5 kg mass you are intelligent relative to a dull student, you are old relative to a child, star is big relative to earth and many more every thing is relative in the world without relative word we can’t express other characteristic so this is important to understand hence we have to study when two body are in motion, in this case one has to move larger distance to catch other body because other body is also moving second body observe that first body is coming towards me see the below picture to understand relative motion here both body are moving.
Relative motion concept analysis
here velocity of body A is 5 m/s and velocity of body B is 4 m/s moving in same direction analyse here initial distance between two body is 5 m after one second A will travel 5 m distance and B will travel 4 m distance now at this moment distance between A and B will be 4 m now in next second again A will travel 5 m and B will travel 4 m hence the distance between them will be 3 m how in 2 second total distance travel by A will be 2*5 = 10 m and by B in 2 second distance travel = 4*2 = 8 m and add 5 m initial separation hence 8+5 = 13 hence separation between them 13-10 = 3 m hence every second A will be closer to B by one meter at the fifth second distance travel by A = 5*5 = 25 m and by B = 4*5 = 20 initial separation is 5 m hence at this moment both A and B will meet now for making this story simple in mathematical formula we suppose that both body taking as a pair and coming closer to each other now imagine as one body is at rest and other body is coming toward rest body but actually both are moving here body B seen body A and observe as body A is coming towards me at speed of 1 m/s body B imagine or experience i am at rest body A is coming towards me 1 m/s speed body B experience again and again body A is coming towards me by 1 m/s and will catch me in 5 second even body B forget i am moving with 4 m/s or body A moving with 5 m/s only body B experience body A is moving towards me by 1 m/s this thought of body B that body A is coming towards me by 1 m/s is relative velocity why relative velocity ? because for any other observer this velocity may be other but for B observer this velocity is 1 m/s and relative velocity is for observer hence in relative velocity we suppose one is observer and other is mover while both is moving so observer imagine that i am at rest and world is moving hence relative velocity is always calculated with respect to an observer this is the way of calculation.
hence B observe A is coming towards it with velocity V𝖆𝖇 here ab notation indicate b is observer and a is mover or b is looking a when a person A observe B then the relative velocity of B observe by A is V𝔟𝔞 so observer always observe other object is moving now calculation and the way of writing here both A and B are moving now velocity of A with respect to neutral body earth Vag here earth surface is at rest for both body when we told my car is moving with speed 60 km/hr then we talk about relative to earth surface which is at rest other car speed is 30 km/hr this is also relative to earth surface which is at rest so Vag is velocity of A with relative to ground surface and velocity of B relative to ground Vbg now Vab = Vag – Vbg hence relative velocity for above case is Vab = 5 – 4 = 1 m/s difference of the velocity suppose both object velocity is same then observer B will observe A is not moving because their difference will be zero while both are moving so observer is always subtracted in above equation and mover is at first place now velocity is vector quantity so we write as
→ → →
Vab = Vag – Vbg now where we use this relative velocity actual we use relative velocity everywhere see how we write and use
Vag = Va -Vg here Vg is velocity of ground surface which is always taken as zero Vg = 0 because earth surface is at rest hence Vag = Va so Va is absolute velocity which is relative to stationary frame of reference we always refer frame of reference as stationary everywhere above earth we are flying in air or on surface of earth we are moving on foot , by car, cycling we assume earth as stationary so for all the practical purpose velocity of earth ground is taken as zero when we will study about space then we will see earth is moving with certain velocity and will be consider at present earth is taken as stationary for our all movement on the surface of earth hence we will write Vag = Va absolute velocity with respect to ground hence we can write our original equation
→ → →
Vab = Va – Vb as simple relative velocity here observer is B if we take A as observe then our equation will be Vba = Vb-Va or
→ → →
Vba = Vb – Va the difference between two equation is only direction when B is observer see the A moving towards right and in case when observer is A see B moving towards left.
Now use of relative velocity we know that time = distance/speed but when two object are moving simultaneously we can’t use above formula because both object are moving hence we use relative speed to determine time now use relative velocity vab = Va – Vb put the value Vab = 5 – 4 = 1 m/s so using this velocity we can find the time when both body will meet now use formula .
time = distance/speed = 5/1 = 5 s here concept is the initial distance between two body is covered by relative speed not cover by actual speed other case if B is not moving then Vb = 0 or in this case A will catch B in just 1 second. hence when two body are moving then we take relative velocity for calculation in simple equation now see question.
Q A jet airplane is travelling with speed 600 km/hr eject its smoke at the speed of 1200 km/hr relative to jet what is speed of latter with respect to observer on the ground.
Ans here jet speed is given respect to ground so it is absolute value Vj = 600 km/hr now smoke speed relative to jet Vsj = 1200 km/hr now we have to find speed of smoke relative to ground hence use relative equation velocity of smoke will be in opposite direction of jet motion.
→ → →
Vsj = Vs – Vj now put the value
1200 = Vs – (-600) or 1200 = Vs +600 0r Vs = 1200 – 600 = 600
Vs = 600 km/hr observer will observe from ground.
Now we will see other case when both body are moving in opposite direction
Both body moving opposite direction .
5 m/s 4 m/s
here A and B are moving in opposite direction then what will be relative velocity take A direction right +ve then B direction left -ve
now apply same formula Vab velocity of A with respect to B
→ → →
Vab = Va – Vb since this is vector quantity sign must be consider.
→ → → → → →
Vab = Va – (-Vb) or Vab = Va + Vb hence when body moving in opposite direction their relative velocity is added means relative velocity will be more and you have seen this practically when two train moving in opposite direction and crosses each other you feel or experience other train is moving very fast because both velocity of train is added which is observed by you is relative velocity.
we will continue some numerical problems in next post.
thanks for reading
Relative motion concept analysis
Dated 29th April 2018