a moving sidewalk in an airport terminal building moves 1.00 m/s and is 150.0 m long.If man steps on at one end and walks 2.0 m/s relative to the moving sidewalk, how much time does he require to reach the opposite end if he walks in the same directions as the side walk is moving?
v=1.00m/s + 2.0m/s = 3.0 m/s
t = 150.0m/3.0 m/s = 50s
to get time, you use the formula X=Xo+Vot+1/2at^2 where X=150
To find the time required for the man to reach the opposite end, we need to calculate the time it takes for him to cover the distance on the moving sidewalk, as well as the time it takes for him to cover the additional distance he walks relative to the sidewalk.
Let's break down the problem and calculate each part separately:
1. Time to cover the distance on the moving sidewalk:
The man is standing on the moving sidewalk, so his effective speed would be the sum of his walking speed and the speed of the moving sidewalk.
Given:
Speed of the moving sidewalk (v_s) = 1.00 m/s
Length of the moving sidewalk (d_s) = 150.0 m
The time required to cover the distance on the moving sidewalk can be calculated using the formula:
Time = Distance / Speed
Time_s = d_s / (v_s + v_man)
Plugging in the values:
Time_s = 150.0 m / (1.00 m/s + 2.0 m/s)
Time_s = 150.0 m / 3.00 m/s
Time_s = 50.0 s
2. Time to cover the additional distance walking at his own speed:
The man walks with a speed of 2.0 m/s, so we need to calculate the time required to cover the extra distance.
Given:
Speed of the man relative to the ground (v_man) = 2.0 m/s
Extra distance walked (d_m) = 150.0 m
Using the same formula:
Time_m = d_m / v_man
Plugging in the values:
Time_m = 150.0 m / 2.0 m/s
Time_m = 75.0 s
3. Total time required to reach the opposite end:
To find the total time, we simply sum up the times taken for both parts of the journey:
Total time = Time_s + Time_m
Total time = 50.0 s + 75.0 s
Total time = 125.0 s
Therefore, the man requires 125.0 seconds (s) to reach the opposite end if he walks in the same direction as the moving sidewalk.