Question

kinematics problm

Escalator Prolelem
on stationary
escalator man reaches to
top in time T1
Standing man on moving escalayor
reaches to top in time T2
If both are moving then find time taken by man reach to top?​

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,

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

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

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

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

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