A ‘moving sidewalk’ in an airport terminal moves at 1 m/s and is 35 m long. If a woman steps on at one end and walks 1.5 m/s relative to the sidewalk, in the same direction as the movement of sidewalk. (a) How much time does it take her to reach the opposite end? 14s (b) What if she steps on the opposite side, walking against the motion of the sidewalk, what must be her speed so that she reaches the end of the track in the same time as in part (a)?
Xo=0...
moving at 2.5 m/s relative to ground
t = 35 m/2.5 m/s
moving at (v-1) m/s
same t
35 = (v-1) t
solve for v
To solve part (b), we need to find the speed at which the woman needs to walk in the opposite direction of the moving sidewalk so that she reaches the end of the track in the same time as in part (a).
In part (a), we know that the woman is moving with a speed of 1.5 m/s relative to the sidewalk, which is moving at a speed of 1 m/s. This means her net speed relative to the ground is 1.5 m/s + 1 m/s = 2.5 m/s.
To find the time it takes for her to reach the opposite end in part (a), we can use the formula:
time = distance / speed
The distance is 35 m and the speed is 2.5 m/s:
time = 35 m / 2.5 m/s = 14 s
So, in part (a), it takes her 14 seconds to reach the opposite end.
In part (b), she is stepping on the opposite side and walking against the motion of the sidewalk. Let's assume her speed is V m/s. The speed of the sidewalk is still 1 m/s, so her net speed relative to the ground is V m/s - 1 m/s = (V - 1) m/s.
We want her to reach the end of the track in the same time as in part (a), which is 14 seconds. So, we can set up the equation:
distance / speed = distance / (V - 1)
35 m / 2.5 m/s = 35 m / (V - 1)
Now, we can solve for V:
V - 1 = 2.5
V = 2.5 + 1
V = 3.5 m/s
Therefore, the woman needs to walk at a speed of 3.5 m/s against the motion of the sidewalk to reach the end of the track in the same time as in part (a).
To solve part (a) of the problem, we can calculate the time it takes for the woman to reach the opposite end of the moving sidewalk.
The woman's speed relative to the sidewalk is the sum of her walking speed and the speed of the moving sidewalk in the same direction. In this case, her relative speed is 1.5 m/s + 1 m/s = 2.5 m/s.
To find the time it takes her to walk 35 meters with a speed of 2.5 m/s, we divide the distance by the speed:
Time = Distance / Speed
Time = 35 m / 2.5 m/s = 14 seconds.
Therefore, it takes her 14 seconds to reach the opposite end of the moving sidewalk.
Now, let's move on to part (b) of the problem. Here, the woman steps on the moving sidewalk from the opposite side and walks against the motion of the sidewalk. We need to find her speed so that she reaches the end of the track in the same time (14 seconds) as in part (a).
Since the woman is moving in the opposite direction of the moving sidewalk, her relative speed will be the difference between her walking speed and the speed of the moving sidewalk. Let's call her walking speed against the motion of the sidewalk "v."
The woman walks a distance of 35 meters in a time of 14 seconds, so we can use the formula again:
Time = Distance / Speed
14 seconds = 35 meters / (v m/s - 1 m/s)
Now, we can solve for v using algebraic manipulation:
14(v m/s - 1 m/s) = 35 meters
14v m/s - 14 m/s = 35 meters
14v m/s = 35 meters + 14 m/s
14v m/s = 49 meters
v = 49 meters / 14 m/s
v ≈ 3.5 m/s
Therefore, the woman must walk at a speed of approximately 3.5 m/s against the motion of the moving sidewalk in order to reach the end of the track in the same time as in part (a) (14 seconds).