An escalator is 15.0 m long. If a person stands on the escalator, it takes 38.0 s to ride from the bottom to the top.
(a) If a person walks up the moving escalator with a speed of 0.500 m/s relative to the escalator, how long does it take the person to get to the top?
(b) If a person walks down the "up" escalator with the same relative speed as in item (a), how long does it take to reach the bottom?
I have no idea what i am doing!
new speed up=.50m/s+15/38 m/s
time= 15/new speed.
newdownspeed=.5-15/38 m/s
time= 15/newdownspeed
No worries! I can help you understand how to solve these problems step by step.
Let's start with part (a), where a person walks up the escalator with a speed of 0.500 m/s relative to the escalator.
To solve this problem, we need to consider the velocities of both the person and the escalator. When a person is standing on the escalator, they are moving at the same speed as the escalator. However, when the person starts walking, their speed is additive to the speed of the escalator.
Here's how you can solve it:
1. Calculate the speed of the escalator:
The length of the escalator is given as 15.0 m, and the time taken to ride from bottom to top is given as 38.0 s. To find the speed of the escalator, divide the length by the time:
Speed of the escalator = 15.0 m / 38.0 s
2. Calculate the total speed of the person walking:
The person's speed relative to the escalator is given as 0.500 m/s. So, the total speed of the person walking is the sum of the relative speed and the speed of the escalator. Therefore:
Total speed of the person walking = 0.500 m/s + Speed of the escalator
3. Calculate the time taken for the person to reach the top:
Divide the length of the escalator by the total speed of the person walking:
Time taken = Length of the escalator / Total speed of the person walking
Now, let's move on to part (b), where a person walks down the "up" escalator with the same relative speed.
The process to solve part (b) is similar to part (a), except that this time the person is moving in the opposite direction to the escalator's motion.
Here's how to solve it:
1. Calculate the total speed of the person walking:
The person's speed relative to the escalator is still 0.500 m/s. However, this time we need to subtract the speed of the escalator, as the person is walking down in the opposite direction of the escalator. Therefore:
Total speed of the person walking = Relative speed - Speed of the escalator
2. Calculate the time taken for the person to reach the bottom:
Divide the length of the escalator by the total speed of the person walking:
Time taken = Length of the escalator / Total speed of the person walking
By following these steps, you can calculate the time it takes for the person to reach the top in part (a) and the time it takes to reach the bottom in part (b).