# Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time t1. On other days, if she remains stationary on the moving escalator, then the escalator takes her up in time t2. The time taken by her to walk up on the moving escalator will be: Option 1) $\frac{t_{1}t_{2}}{t_{2}-t_{1}}$ Option 2) $\frac{t_{1}t_{2}}{t_{2}+t_{1}}$ Option 3) $t_{1}-t_{2}$ Option 4) $\frac{t_{1}+t_{2}}{2}$

As we learnt in

Case of Relative velocity -

When A & B are moving along with straight line in opposite direction.

$\vec{V}_{A}=$ Velocity of object A.

$\vec{V}_{B}=$ Velocity of object B.

Relative velocity of A with respect to B is.

$\vec{V}_{AB}=\vec{V}_{A}-(-\vec{V}_{B})$

$-\vec{V}_{B}$  is because of opposite direction.

$\vec{V}_{AB}=\vec{V}_{A}+(\vec{V}_{B})$

- wherein

E.g A body moves in east with speed of 20m-1, And body in west with velocity of 5ms-1.

Find velocity of A with respect to B.

$\vec{V}_{AB}=\vec{V}_{A}+(\vec{V}_{B})$

= (20+5 ) ms-1

= 25 ms-1

$V_{1}=$  Velocity of Preeti

$V_{2}\rightarrow$ Velocity of escalator

$l\rightarrow$ distance

$t= \frac{l}{v_{1}+v_{2}}=\frac{l}{\frac{l}{t_{1}}+\frac{l}{t_{2}}}$

$=\frac{t_{1}t_{2}}{t_{1}+t_{2}}$

Correct option is 2.

Option 1)

$\frac{t_{1}t_{2}}{t_{2}-t_{1}}$

Incorrect

Option 2)

$\frac{t_{1}t_{2}}{t_{2}+t_{1}}$

Correct

Option 3)

$t_{1}-t_{2}$

Incorrect

Option 4)

$\frac{t_{1}+t_{2}}{2}$

Incorrect

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