Motion is a combined property of the object under study as well as the observer. It is always relative ; there
is no such thing like absolute motion or absolute rest. Motion is always defined with respect to an observer
or reference frame.
Relative Position
It is the position of a particle w.r.t. observer
Definition : Relative velocity of a particle A with respect to B is defined as the velocity with which A
appears to move if B is considered to be at rest. In other words, it is the velocity with which A
appears to move as seen by B considering itself to be at rest.
Relative Acceleration
It is the rate at which relative velocity is changing.
It is the component of relative velocity of one particle w.r.t. another, along the line joining
them.
position of A with respect to O
B r = position of B with respect to O
rAB = position of A with respect to B.
Relative Motion in Lift
Projectile motion in a lift moving with acceleration a upwards
If a man can swim relative to water with velocity mR v ï² and water is flowing
Velocity of river is u & velocity of man in still water is v.
Case - 1
Man swimming downstream (along the direction of river flow)
Consider a man swimming in a river with a velocity of MR v ï² relative to river at an angle of ? with
the river flow
Consider a man swimming in a river with a velocity of MR v ï² relative to river at an angle of ? with the
river flow
It is defined as the displacement of man in the direction of river flow. (see the
figure).
i.e. time to cross the river will be minimum if man swims perpendicular to the
The minimum possible drift is zero. In this case the man swims in the direction
perpendicular to the river flow as seen from the ground. This path is known as
shortest path
This is very similar to boat river flow problems. The only difference is
that boat is replaced by aeroplane and river is replaced by wind
If rain is falling vertically with a velocity R v ï² and an observer is moving horizontally with
velocity m v ï² , the velocity of rain relative to observer will be
It is the component of relative velocity of one particle w.r.t. another, along
the line joining them.
If two particles are moving with uniform velocities and
the relative velocity of one particle w.r.t. other particle is
directed towards each other then they will collide.
If the separation between two particles decreases and after some
time it starts increasing then the separation between them will be
minimum at the instant,
