Q31E - University Physics with Modern Physics

Question

A “moving sidewalk” in an airport terminal moves at 1.0 m/s and is 35 m long. If a woman steps on at one end and walks at 1.5 m/s relative to the moving sidewalk, how much time does it take her to reach the opposite end if she walks (a) in the same direction the sidewalk is moving? (b) In the opposite direction?

Step-by-Step Solution

Answer

1. The time taken by a woman to reach the opposite end of the sidewalk moving in the same direction is 14 s.
2. The time taken by a woman to reach the opposite side of the sidewalk moving in the opposite direction is 70 s.

Step 1: Identification of given data:

The given data can be listed below.

• The speed of the sidewalk is, v_s = 1m/s 
• The length of the sidewalk is, d = 35m 
• The relative speed of a woman with respect to the sidewalk is, v_ws = 1.5m/s 

Step 2: Concept/Significance of relative speed:

The relative speed is equal to the difference between the speeds of two objects traveling in the same direction at different speeds. 

 Their relative speed is equal to the total of their speeds if they are going in the opposite direction.

Step 3: (a) Determination of time taken by women to reach the opposite end if she walks in the same direction the sidewalk is moving:

The woman's net velocity would equal the sum of the two velocities if she were going in the same direction as the sidewalk's motion given by,

v_nw = v_s+v_ws

Here, v_s is the velocity of the sidewalk and v_ws is the velocity of the woman.

Substitute all the values in the above,

$\begin{array}{rcl}{v}_{nw}& =& 1.5m/s+1m/s\\ & =& 2.5m/s\end{array}$

The time taken by woman to reach other side of sidewalk is given by,

$t=\frac{d}{v}$

Here, d is the length of the sidewalk and v is the velocity of woman.

Substitute all the values in the above,

$\begin{array}{rcl}t& =& \frac{35m}{2.5m/s}\\ & =& 14 s\end{array}$

Thus, the time taken by woman to reach the opposite end of sidewalk moving in same direction is 14 s.

Step 4: (b) Determination of time taken by women to reach the opposite end if she walks in the opposite direction the sidewalk is moving:

The net velocity of a woman when moving opposite direction to the sidewalk is given by,

v_nw = v_ws - v_s

Here, v_s is the velocity of the sidewalk and v_ws is the velocity of the woman.

Substitute all the values in the above,

$\begin{array}{rcl}{v}_{nw}& =& 1.5m/s-1m/s\\ & =& 0.5m/s\end{array}$

The time taken by a woman to reach other side of the sidewalk is given by,

$t=\frac{d}{v_{nw}}$

Substitute all the values in the above,

$\begin{array}{rcl}t& =& \frac{35m}{0.5m/s}\\ & =& 70s\end{array}$

Hence, the time taken by a woman to reach the opposite side of the sidewalk moving in the opposite direction is 70 s.