Relative velocity is the
comparative velocity of one body with respect to other body. One body will have
a relative velocity with respect to other one only when there is a relative
motion between them. If two bodies are having the motion in the same direction
relative velocity of one with respect to other is the difference between them.It is simply because one bodies having more velocity when compared with the
other body and how much more can be obtained only by subtracting that from the
other value.
If two bodies are travelling in
the opposite direction we can incorporate the same concept but being the bodies
are in the opposite direction the resultant will become automatically the some
of the two vectors as shown.
If two vectors are having an
angle between them to find the relative velocity between them we shall
incorporate a third body in between them. Generally the third body is the
ground.
Expressing velocity of the
any body with respect to ground is more appropriate than expressing the velocity
of the ground with respect to other body.It is simply because it is not
the ground that is moving but the body moving on the ground.
Problem and Solution
Basing on a
relative motion of two bodies. Let us consider two bodies each having the
same velocity 10 m/s,one moving along the east other moving along the north
from the same point. Find the relative velocity of one body with respect to
other body?
While we are solving the problem
we need to take a reference and the ground into consideration as reference.After
identifying the answer,we can
identify the direction of the vector.
Problem
The person is walking in the rain
feel that the velocity of the rain is as twice as his velocity. It which angle
you should hold his umbrella with vertical if he’s moving in a forward
direction and training is happening in a vertical downward direction therefore
he cannot be drenched in the rain?
Solution
This problem can also be solved
basing on the concept of relative velocity as shown below. Whenever requirement
of the third body is there we always get the ground into consideration because
it is always there. We prefer to say the velocity of the body with respect to
ground than in the reverse way because
bodies move on the ground.
Motion of a boat in a river
There are four different possible
pace of about moving across the river.
Case one
When a boat is crossing
the river along the direction of the river:
In this case the motion of the
boat is bit easy because it is supported by the stream of water therefore the
boat takes less time to cross the river.
Case two
Let us consider a case
that the boat is moving against the steam of the river. In this case as boat has to
overcome the opposition of the river it takes more time.
Case three
Let us consider a
case boat has to cross the river in such a way that it has to reach the exact
opposite position.In this case we are actually not going along the river but
where crossing the river.
If you travel straight to the opposite point as the
river pushes you are not going to reach the exact opposite point. That’s why we
shall drive river boat with an angle with
the vertical.
In the following derivation we have discussed the that with what
angle he shall drive therefore he will be reaching the exact opposite point.In
this case you are going to reach the exact opposite point means the path is the
shortest but it is going to take the longest time to cross the river.
Case four
In this case boat will
go straight to the opposite point and being the river is going to push it it is
not going to reach the exact opposite point but some other point in the bank of
the river. In this case the party is going to be longest but the time is going
to be shortest.
So here we have two choices.When
you want to cross the river and the shortest path we have two choose case three
where as when you want to cross the river with the shortest time we had to
choose case four.
Case five
Suppose you are
crossing the river in such a way that you are making an angle with the vertical, but it is not sufficient
to reach the exact opposite position.
In this case we have resolve the
component of velocity of the boat along a horizontal and vertical parts. The
vertical part will help you to identify the time taken to cross the river
whereas the horizontal component of velocity has to be subtracted from the
velocity of the river value while calculating the drift of the water. Drift is
simply a particular value of the displacement because of which the boat has
missed the exact opposite position. The equation for this drift is as shown.
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