Question

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Answer 1

Let s be the length of the escalator.

Case 1:- Man is moving on stationary escalator

The man reaches top only by velocity of the man and he reaches in time $\displaystyle\sf {t_1.}$

The velocity of the man will be given by,

$\displaystyle\mathbf{v_1}=\mathsf{\dfrac {s}{t_1}}$

Case 2:- Man is stationary on moving escalator

The man reaches top only by velocity of the escalator and he reaches in time $\displaystyle\sf {t_2.}$

The velocity of the escalator will be given by,

$\displaystyle\mathbf{v_2}=\mathsf{\dfrac {s}{t_2}}$

Now consider the case when both man and escalator are moving.

Both the man and the escalator are moving in same direction. The man reaches top with resultant velocity of man and escalator, i.e., $\displaystyle\mathbf {v_1+v_2}.$

Then time taken by man to reach the top will be,

$\displaystyle\mathsf{\longrightarrow t=\dfrac {s}{\mathbf{v_1+v_2}}}$

$\displaystyle\sf{\longrightarrow t=\dfrac {s}{\dfrac {s}{t_1}+\dfrac {s}{t_2}}}$

$\displaystyle\sf{\longrightarrow t=\dfrac {s}{s\left [\dfrac {1}{t_1}+\dfrac {1}{t_2}\right]}}$

$\displaystyle\sf{\longrightarrow t=\dfrac {1}{\left [\dfrac {t_1+t_2}{t_1t_2}\right]}}$

$\displaystyle\sf {\longrightarrow\underline {\underline {t=\dfrac {t_1t_2}{t_1+t_2}}}}$

Answer 2

Answer:

your answer

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