Solve these two questions
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Answers
RELATIVE VEL RELATIVE VEL TIVE VELOCITY
Definition : Relative velocity of a particle (object) A with respect to B is defined as the velocity with which A
appears to move is B if considered to be at rest. In other words, it is the velocity with which A appears to move
as seen by the B considering itself to be at rest.
Relative motion along straight line -
vA
= dt
dxA
, vB
= dt
dxB
xBA = xB
– xA
vBA = dt
dxB
– dt
dxA
vBA = vB
– vA
⇒ vAA = vA
– vA
= 0 (velocity of A with respect to A)
Note : velocity of an object w.r.t. itself is always zero.
Ex.1 An object A is moving with 5 m/s and B is moving with 20 m/s in the same direction. (Positive x-axis)
(i) Find velocity of B with respect to A.
Sol. vB
= 20 i
ˆ m/s ⇒ vA
= 5 i
ˆ m/s ⇒ vB
– vA
= 15 i
ˆ m/s
(ii) Find velocity of A with respect to B
Sol. vB
= 20 i
ˆ m/s, vA
= 15 i
ˆ m/s ⇒ vAB = vA
– vB
= – 15 i
ˆ m/s
Note : vBA = – vAB