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Grade 11Mechanics

A person walks up a stationary escalator in 90 sec. If the escalator moves with thee person first standing on it it will take 1 minute to reach the top. How much time it would take him to walk up with the moving escalator.
First of all I solved it in the following way

Vmg = Velocity of man wrt ground = + L/90 where L is length covered
Vme = Velocity of man wrt escalator = ??
Veg = Velocity of escalator wrt ground = +L/60

So as per the equation given in HC Verma
Vmg= Vme + Veg
Vme= Vmg – Veg = L/90 – L/60 = -L/180

But the answer is L/36 how
(NOTE: I am highly disappointed by this website as it is the most disgusting one I have ever seen. Doubts are cleared very late , you are persuaded to buy the products instead and listen to me please don't to just show the solution please explain as to why the actual velocities are getting added and not getting subtracted as we do in other cases of relative motion. Many of my questions haven't been answerd I have to surf other websites what is the use of getting registered then here. You people are helping very less in very little amount. PLEASE HELP )

Pritesh Ramya

10 Years agoGrade 11

2 Answers

Frank Hank

9 Years ago

v1 = walking speed of person v2 = escalator speed The person walks up the stationary escalator (length L) in 90s. L = speed x time = 90v1 The escalotr moves a distance L in 60s. v2 = distance/time = L/60 = (90v1)/60 = 1.5v1 When walking up the escalator, the person`s speed = v1 + v2. time taken = distance/speed t = L / (v1 + v2) t = 90v1/(v1 + v2) Substituting for v2: t = 90v1/(v1 + 1.5v1) = 90 / (1 + 1.5) = 90 / 2.5 =36 s

Gowtham

7 Years ago

V1=walking speed of person , v2=escalator speed .

Time taken for the man to walk up stationary escalator is 90sec. Distance travelled in moving escalator (length L) is

Distance=speed × time. Speed= distance/time ,V1=L/90sec-------- 1st equation.

Time taken for which escalator is moved is 60sec. Distance travelled in moving escalator is (length L) is,

V2=L/60sec ----------- 2nd equation.

Distance travelled by the man to walk up moving escalator is(length L).

Time taken for the man to walk up moving escalator is

Time =Distance/(V1+V2),=L/(L/90sec+L/60sec)

=L/(L(90+60)/90×60)=L×5400/L(150)=5400/150=36sec

(Taking L.C.M and transporting it to up ),(Taking L common and cancelling it ).

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