Answer

Verified

402.3k+ views

**Hint:**Use the relation between the velocity, displacement and time to determine the speeds of escalator and person separately. Add these two speeds to obtain the combined velocity. Again, use the relation between the velocity, displacement and time to determine the time.

**Formula used:**

\[ \Rightarrow v = \dfrac{d}{t}\]

Here, d is the distance and t is the time.

**Complete step by step answer:**

Suppose \[d\] is the distance that the person wants to travel through the escalator to reach the top of the tower.

We know the relation between velocity, distance and time. The velocity of the body is the distance d divided by time t.

\[ \Rightarrow v = \dfrac{d}{t}\]

The speed of the escalator is,

\[{v_1} = \dfrac{d}{{{t_1}}}\]

Here, \[{t_1}\] is the time taken by the person to reach the top of the tower using a moving escalator.

The speed of the walking person over an escalator is,

\[ \Rightarrow {v_2} = \dfrac{d}{{{t_2}}}\]

Here, \[{t_2}\] is the time taken by the person to reach the top of the tower by walking.

The speed of the person while walking on the moving escalator is the sum of the above speeds.

Therefore,

\[ \Rightarrow v = \dfrac{d}{{{t_1}}} + \dfrac{d}{{{t_2}}}\]

\[ \Rightarrow v = d\left( {\dfrac{1}{{{t_1}}} + \dfrac{1}{{{t_2}}}} \right)\]

time taken by the person to reach the top of the tower with this speed is,

\[ \Rightarrow t = \dfrac{d}{v}\]

\[ \Rightarrow t = \dfrac{d}{{d\left( {\dfrac{1}{{{t_1}}} + \dfrac{1}{{{t_2}}}} \right)}}\]

Rearrange the above equation as follows,

\[ \Rightarrow t = \dfrac{1}{{\dfrac{{{t_1} + {t_2}}}{{{t_1}{t_2}}}}}\]

\[ \Rightarrow t = \dfrac{{{t_1}{t_2}}}{{{t_1} + {t_2}}}\]

**So, the correct answer is option (D).**

**Note:**In this question, the distance to be traversed is the same for both cases. Therefore, do not take different distances for the distance travelled by the person through escalator and the distance travelled by the person by walking.

Recently Updated Pages

Draw a labelled diagram of DC motor class 10 physics CBSE

A rod flies with constant velocity past a mark which class 10 physics CBSE

Why are spaceships provided with heat shields class 10 physics CBSE

What is reflection Write the laws of reflection class 10 physics CBSE

What is the magnetic energy density in terms of standard class 10 physics CBSE

Write any two differences between a binocular and a class 10 physics CBSE

Trending doubts

Difference Between Plant Cell and Animal Cell

Mention the different categories of ministers in the class 10 social science CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Who is the executive head of the Municipal Corporation class 6 social science CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Which monarch called himself as the second Alexander class 10 social science CBSE

Select the word that is correctly spelled a Twelveth class 10 english CBSE

Write an application to the principal requesting five class 10 english CBSE