JEE Physics/ Lakshmikanta Satapathy/ Kinematics QA part 11/ Question on relative velocity involving a man and an escalator when either or both are in motion solved with the relates concepts

1. Physics Helpline
L K Satapathy
Kinematics QA 11
Relative velocity
S
A
B

2. Physics Helpline
L K Satapathy
Kinematics QA 11
Question : A man standing on an escalator takes time to reach the top of a tower
when the escalator is in motion and takes time to walk up when the escalator is
not moving. Then the time taken by him to walk up the moving escalator is
(a) (b) (c) (d)1 2t t 1 2t t 1 2
1 2
t t
t t
1 2
1 2
t t
t t
1t
2t
Answer :
S
A
B
Case-1: Only the escalator is moving and the man
is not walking. Time taken = t1
Case-2: Only the man is walking on the escalator
and the escalator is not moving. Time taken = t 2
Case-3: The man is walking on the escalator and
the escalator is also moving. Let time taken = t
We are required to find the value of t

3. Physics Helpline
L K Satapathy
Kinematics QA 11
Let the distance AB = S
Walking speed of the man = u
Speed of the escalator = v
Case-1:
Distance covered = S and time taken = t1
0 , 0ME EG MG ME EGv v v v v v v v       
1
1
. . . (1)SS vt v
t
  
We will use the following relative velocity notations :
(i) Velocity of Man relative to escalator = v ME
(ii) Velocity of Escalator relative to Ground = v EG
(iii) Velocity of Man relative to Ground = vMG
 vME + vEG = vMG

4. Physics Helpline
L K Satapathy
Kinematics QA 11
Case-3:
Distance covered = S and time taken = t
(1) , (2) and (3) 
Correct option = (d)
,ME EG MG ME EGv u v v v v v u v      
( ) . . . (3)SS u v t u v
t
    
1 2
S S Su v
t t t
   
1 2
1 2
[ ]
t t
t
t t
Ans 

1 2
1 2 1 2
1 1 1 t t
t t t t t

   
Case-2:
Distance covered = S and time taken = t2
, 0 0ME EG MG ME EGv u v v v v u u       
2
2
. . . (2)SS ut u
t
  

5. Physics Helpline
L K Satapathy
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