Hello everyone, welcome back to a new video.
The topic we are going to discuss in today's video, as I
told you in the last video, is the topic of Relative Speed.
Till now, we have done average speed.
We have done different cases, that if any of the three,
speed, distance and time, if anything becomes constant,
then what is the relation with the other?
What is the proportionality?
We have done that.
So, whatever questions we have seen till now, or whatever
examples I have given you, in those, there was a particular
object, whose speed we used to talk about, we used to take
the case of that only, or we used to take the case of the
other object.
We did not submerge both of them.
But what will happen in Relative Speed?
We will see the speed of two moving objects.
The speed of two moving objects, with respect to whom?
Not alone or alone.
Till now, we were saying that, one boy A is moving at one
speed, and boy B is moving at another speed.
And then all their cases, which we have asked in the
question. But now, what will happen with us? That A is
moving, and B is also moving.
Both are moving.
We have to tell the speed of A, with respect to whom?
With respect to the other moving body, that is, with
respect to B.
So, what do we call that speed? We call that speed as
Relative Speed.
When we calculate the speed of one moving object, with
respect to another moving object, we will call that as
Relative Speed. Okay? You understood the basic concept of
Relative Speed. Now, what cases will we have?
For example, if you see, if two people are running, if two
things are running together, running in the same direction,
then what will happen?
You will feel that, if you have the same speed, then you
will feel that, we are not moving at all.
Both are moving together.
So, with respect to them, what is the speed of both?
It is the same.
So, with respect to them, there is no difference in their
speed, if they are moving together.
But, if you feel the same case, that you are going
somewhere else, you are running in opposite direction,
opposite direction as in, you are running separately, one
is running on one side, and the other is running on the
other side.
So, how quickly you are separating from each other, you are
departing, means, the distance between you is increasing.
Means, your speed, if in one's relation, with respect to
one, we are taking out the speed of the other, means, we
are taking out the speed of one, with respect to person B,
so, what we feel is, what is happening in their speed?
Their speed is increased.
Means, it is more speed.
Because, they are moving away quickly.
So, what we see is, what is their speed?
It has increased.
So, these are your two cases.
What will happen in your two cases, in your relative speed?
That, either you are moving in different direction, means,
you are coming close, or you are moving away.
So, for this, the first thing you have to understand is,
you will need to understand the direction.
As you know the direction, we have four directions.
What are the directions?
This one is your North.
This is your South.
This is your East.
This is your West.
These are your directions,
North, East, South, West.
So, what we will see is, the first case, which will be in
your relative speed, case 1.
Isn't it? Case 1.
Let us suppose, there is a boy here.
There is a girl here.
Okay? Both of them are in long distance.
After a long time, they are meeting each other.
After a long time, when they are meeting each other, while
running, they will come to hug each other.
Right? They will come to meet each other.
They will come to greet each other.
So, both of them are running at some speed.
And, the boy is also running at some speed.
So, what will we find in this?
If we find the relative speed of boy with respect to girl,
or relative speed of girl with respect to boy, then how
will we find that?
We can understand it in this way, that we take the speed of
this, let us take the speed of girl, which is constant.
Isn't it?
Take the speed of one moving object, which is constant,
that it is standing at one place.
And, the other one is running.
Okay? If, let us suppose, the speed of our boy is x km per
hour.
And, what is the speed of our girl?
Okay, do not look at km per hour.
You can look at it in small units.
Meter per second, x meter per second, is the speed of boy.
And, what is the speed of girl? y meter per second.
Now, see, in which direction boy is running?
If we see this direction, then boy is running in this
direction.
Normally, I am telling you, that in this direction.
If he is coming here, then he is running in this direction.
And, in which direction is girl running?
Girl is running in the west direction.
In the west direction.
So, if we see their concept direction wise, then what is
the direction?
In which direction both are moving?
In the opposite direction.
Now, you will say,
Ma'am, how in the opposite direction?
Both are coming close.
So, they are moving towards each other.
So, they are coming close, but if we talk about direction
wise, that what is the direction?
So, the direction is opposite to both.
They are running in the opposite direction.
She is running in this direction.
So, the direction is opposite to them.
No doubt, they are coming close to each other.
But, what is the direction?
Opposite.
So, this case is opposite direction case.
Opposite direction.
What is opposite direction?
When objects are moving in opposite direction.
Means, if we are taking the case of two objects, then what
are those two objects moving?
They are moving in opposite direction.
Now, when this boy and girl will run, then what will happen?
Their distance will be less.
We will feel that they are coming close to each other.
So, what is the speed?
Their speed will increase.
If we consider one as constant, then the speed with which
the boy will increase, will increase with the speed with
which they will add up.
So, relative speed in this case, which is opposite
direction case, what will be the relative speed?
Relative speed would be,
Relative speed of one object, we will not write relative
speed as it is.
We will write relative speed of a person with respect to
another person.
So, what will happen?
Relative speed of boy, with respect to girl.
In the respect of girl.
Means, in the respect of girl, we will consider it as
constant.
So, let us suppose, girls are at constant, and we are
taking the speed of boy.
So, what will happen?
The sum of their individual speed.
x plus y.
And, the unit of both the speed is same.
Meter per second.
If it is kilometer per hour, then it is kilometer per hour.
So, relative speed, if it is in opposite direction, then
what will happen?
Our individual speed will add up.
Did everyone understand this much?
So, this is case 1, when in opposite direction, when bodies
are moving in opposite direction.
Bodies are moving in opposite direction.
So, this is your case 1.
Now, case 2.
When bodies are moving in, when bodies, your objects, are
moving in same direction.
Same direction.
What does same direction mean?
The same direction I told you, that if one person is moving
in east direction, then other person is also moving in east
direction.
Means, both are moving in same direction.
In this, what example can you think of?
For example, car or race.
If two people are racing, car is racing, anyone is moving
in same direction.
So, they are moving in same direction.
Parallel.
So, that will be its example.
And, if you see its example in boy and girl's respect.
The last example we did, if this is boy, and this is girl,
what will happen to them?
If there is no contradiction, then what will happen?
If girl is running this way, then boy will go behind her to
pacify her.
So, boy will also run in same direction.
With his speed.
Whatever is his particular speed.
So, what will happen is, in which direction both are going?
Both are moving in same direction.
So, when our bodies will move in same direction, then in
that case, what will be the formula of relative speed?
Relative speed of...
boy with respect to we are using example of boy and girl
similarly, first body with respect to second object body,
object, person with respect to car or train with respect to
another thing, you write that in first and second then what
will happen our
speed, individual speed will be different now what will be
the difference speed of boy will be speed of girl will be
speed of boy will be more than speed of girl so we don't
know speed of boy will be more than speed of girl so as a
formula we write mod
x-y mod means whatever will be the value of difference you
have to take it as positive and then whatever will be the
unit you can write unit as km per hour or m per second so
this will be x, speed of boy and y, speed of girl so speed
of both will be different
this will be our relative speed now we have objects and
bodies moving in same direction so this was the concept of
relative speed next we will do some questions see this read
the question question says it takes 8 hours for a 600 km
journey it takes 8
hours for a 600 km journey it takes 8 hours for a 600 km
journey it takes 8 hours for a 600 km journey total journey
of 600 km if 120 km 120 km is done by train and the rest by
car if 120 km is done by train then the rest of the
distance is covered by
car so total distance
total distance of journey of journey of 600 km and it is
completed in 8 hours and it is completed in 8 hours when is
it needed to complete in 8 hours when we are covering when
we are covering by train 120 meters we are covering by
train and rest, how
much rest is left?
Rest will be 600 minus 120 because total distance is 600.
So from that we will minus the journey by train.
So with whom we are covering that? We are covering it by
car.
So this will be how much? 600 minus 120 that is 480
kilometers by car.
We are covering it by car. So this was our data till here.
Then it takes 20 minutes more if 200 kilometers is done by
train.
So one case we have got that 8 hours.
Then what is the second case we have?
Now how much time we are taking? 8 hours, 8 hours are
taking plus 20 minutes more.
Plus 20 minutes, when is this happening?
When we are covering this distance, we are doing 200
kilometers by train.
And rest, how much rest is left? 400.
400 kilometers because total distance is 600.
600 kilometers is the journey. So 400 we are covering by
car.
So this was our data which we have taken from the questions.
So what has been asked?
The ratio of speed of train to that of a car.
Speed of train, ratio speed of car we have to find.
So what we will do in this question? First of all we will
let speed of train.
We let speed of train as x kilometer per hour.
And we let speed of car as y kilometer per hour.
We can let this much.
Then what we will do? We will find out their ratio.
But how we will do this?
Speed, think once, till then I will write the solution here.
You write this, speed of car is equal to x kilometer per
hour.
And speed of train is x kilometer per hour.
And speed of car is y kilometer per hour.
Now you see in this one question that what is same we have?
If we see this first case.
What we have in first case? Let me change the color of pen.
What we have in first case?
That it is doing 120 kilometer distance from train.
Right? So suppose it took time.
It must have taken some time. Let us suppose it took t1
time.
And it took t2 time from this.
Now this t1 time taken from train and t2 time taken from
car.
What will be the addition of these two times? t1 plus t2.
What will it give us?
The time which will be taken from train and car.
That will be total time which we have to complete the
journey.
So total time will be equal.
And how much time we have taken?
It took 8 hours.
So what will be the addition of t1 and t2?
What will we get? 8 hours.
So we will write this first that t1 plus t2.
What will we get? 8 hours.
Now how to subtract t1 and t2?
Now we have let the speed of train and distance from train.
That we have covered this much distance from train.
So we will take out time when speed and distance are given.
So we will take out time.
What will be the time?
Distance upon speed.
Time will be distance upon speed. So distance is 120
kilometer.
And what is our speed?
How much speed we have let?
We have let speed as x kilometer per hour.
x kilometer per hour.
Kilometer to kilometer cancel.
So our time will be in hour.
So it will be 120 by x hour.
We will write unit later.
Plus t2. Similarly we will subtract t2.
What is the distance? 480 for car.
And what is its speed? Its speed is y.
So what will happen?
It will be equal to 8 hours.
Now let it be like this.
Now what will we get from second case? In second case also
do the same.
That time will be given t3 and t4 time.
So t3 plus t4 we have to give total time.
Now what is the total time? 8 hours plus 20 minutes.
Now we cannot write 8 hours plus 20 minutes.
Let us convert it into one unit.
So it is in hours because it is in kilometer.
So let us change it into hours.
What will happen? 8 hours is in hours.
How can we write 20 minutes?
It is one third of hour.
60 minutes.
So it is one third of 60.
So what will happen? 8 hours plus one third hour. So this
is the total time.
If we solve this, what will happen? 25 by 3 hours.
So the time of second case is 25 by 3 hours.
So put these values.
What will we get from second case? This is from first case.
This will come from second case.
That is t3 plus t4 would be equal to 25 by 3 hours.
So what is this?
What was its distance? 200 by x plus 400 by y is equal to
25 by 3.
Now we have two variables x and y.
And we have two equations.
So to find out two variables, minimum two equations are
required.
So by solving these two, we will get the value of x and y.
So let us start.
First let us make coefficient of x equal to 1.
To make coefficient of x equal to 1, we have to divide
equation 1 by 120. And to divide equation 2 by 120,
So, if we are dividing this with 120, then what will it
become? 1 by x plus, if we divide this with 120, then 120
force the 4 by y is equal to 8 by 120.
Solve 8 by 120, what will it become? 1 by 15, so this would
be 1 by 15.
This is your main equation.
Then, if we divide this second one with 200, then what will
it become? 1 by x plus 2 by y is equal to 200, 25 by 3 into
200.
So, this is 25 times 1 and 25 times 4, which is 8.
So, this becomes 1 upon 24.
This is your second equation.
Subtract from first and second equation because 1 by x and
1 by x is common.
So, this equation minus this equation, 1 by x and 1 by x
will cancel out.
What will it become?
This would be, what was your equation? 1 by x plus 4 by y,
4 by y is equal to 1 by 15.
And, second equation was 1 by x plus 2 by y is equal to 1
by 24.
So, if we subtract this, the sign will change here.
See, 1 by x and 1 by x cancel out.
4 by y minus 2 by y, what will it become? 2 by y, because
it is same as LCM, yy.
And, what will it become? 1 by 15 minus 1 by 24.
Okay? Solve this 15 into 24.
What will it become? 24 minus 15, that would be 9.
9 upon 15 by 24.
This is cancelled out from 3.
3 by 3 is 3 times 5.
So, this is 3 times 1, 3 times 8.
So, 1 by 40.
1 by 40.
So, what is the value of 2 by y? 1 by 40.
So, what is the value of y? 1 by 40.
So, what is the value of y?
From 2, it will go here.
Multiply, so we get y.
80.
What is y? 80.
It was speed, so it came at 80 kmph.
Now, in any equation, in any of these two equations, if you
add the value of y, you will get the value of x.
So, let's add in this one, in the second one.
So, what will it become?
If y becomes 80, then 1 by x is equal to 1 by 24 minus 2 by
80.
That is 1 by 40.
So, take their LCM.
Now, multiply it.
40 minus 24, that would be 16.
16 is cancelled out.
4 tens, 4 fours, 4 ones, and 4 sixes.
So, this becomes 1 by 60.
So, what is the value of x? 1 by x is equal to 1 by 60.
So, below, 1 is equal to 1.
So, x would be equal to 60.
So, the value of x is 60 kmph.
Now, we had to find the ratio of these two.
Whose? Train's.
So, if we do x ratio y, then x ratio y would be 60 ratio
80, or 60 by 80.
That is, it is cancelled out.
3 by 4.
So, what is the ratio we have? 3 is to 4.
So, what was asked in the question?
What was asked in the question?
The question was asked, the ratio of speed of train.
So, what was the answer of x ratio y? 3 is to 4.
3 ratio 4.
I hope you would have understood this question clearly.
How did we do it?
On the same line, same formula is related.
This is your question.
I will give this in the homework, but I will explain a
little.
The distance between Delhi and Mumbai is 440 km.
This is Delhi.
This is our Delhi.
And this destination is our Mumbai.
What is the distance between these two destinations? 440 km.
A train starts from Delhi.
A train is starting from Delhi with a speed of 60 km per
hour.
And a train is starting from Mumbai at the same time.
At the same time, if it is 8 o'clock, then it is 8 o'clock.
If it is 9 o'clock, then it is 9 o'clock.
Both are starting at the same time.
Its speed is 50 km per hour.
Now, both will go from the same way.
So, they will cross each other somewhere.
So, suppose they will cross somewhere.
So, after how much time trains will meet?
So, wherever it will cross, at what time it will reach
there?
We have been asked that.
So, how will you find this?
Now, whatever is the distance, 440 km, you can split it.
Let us suppose that when we started, at an initial time,
let us suppose we started at 12 o'clock.
At what time did the train start from both places?
At 12 o'clock.
So, from 12 o'clock, after some time, let us suppose we
found this, after some time, so it covered the distance of
x km.
Now, the train which started from Mumbai, it covered the
distance of y km.
We can take y, but we will not take y.
When we have only one variable, when it covered the
distance of x km, then what will be the remaining distance?
The remaining distance will be total minus x.
So, we will have 440 minus x km.
So, Mumbai train covered this much distance, and Delhi
train covered this much distance.
Now, whenever they met, they must have met at the same time.
That means, if it took 5 hours, then it must have travelled
for 5 hours, then it must have met at a common point.
So, the time taken to meet at this point, that will be same
for both.
Now, when their time is same, distance is given, speed is
given, then what should be done to their time?
Equate their time.
So, x km, I will give you an equation, what will happen?
It covered x km at this speed.
So, the time taken will be same for both.
So, what is your time?
x km per hour.
It covered distance x km.
And this is the speed.
So, what is your time?
Time.
Your time will be speed.
What will be the time?
Distance upon speed.
So, distance is x, speed is 60 km per hour.
Similarly, this will be...
What is this? 440 minus x, this is the distance.
And what is the speed in this?
Speed is 50 km per hour.
So, distance upon speed will be the time.
Now, this and this should be equal, because time is same.
So, how will we do the time?
For 40, minus x upon 50 would be equal to x by 60.
If we solve, then what will happen? 0 and this would be 24,
24, 26, 2640. 2640 minus x is equal to 5x.
So, 2640 is equal to 6x.
So, what will be the value of x?
Divide by 6.
So, 4x, 4x, this will be 440.
How is 440 coming?
Sorry, sorry.
This will be 6x.
440 is the total distance.
So, what will be this? 6, this will be multiplied by 6x.
So, this will be 11x.
So, 2640 divided by 11.
So, what will be the value of 11 divided by 11? 2 is equal
to 22.
So, x will be 2, 22, and 44, 4.
So, 240 km is the distance.
So, Delhi train has covered 240 km.
And how much will it cover? 440 minus, 240.
So, what will be this?
It has covered 240 km.
And how much has it covered? 200 km.
So, we have to find the time.
So, keep the value of x in any equation.
I hope you have understood the concept of relative speed,
distance and time.
Now we will do miscellaneous questions on trains in the
next videos.
Thank you for watching.
Goodbye.