An escalator is 20 m long. If a person stands on the 'up' side, it takes 50 seconds to ride to the top.

a) If a person walks up the escalator at a speed of 0.5 m/s relative to the escalator, how long wil it take to get to the top?
b) If a person walks down the 'up' side at the same relative speed as in (a), how long will it take to arrive at the bottom?

ride speed = 20 m/50 s = .4 m/s

total speed = .4 + .5 = .9

t = d/speed = 20/.9 = 200/9 = 22.2 seconds

part b
speed = .5 - .4 = .1
20/.1 = 200 seconds

a) Well, let's do the math with a smile! When a person walks up the escalator, their speed relative to the ground is the sum of their walking speed and the escalator's speed. In this case, 0.5 m/s + the speed of the escalator. Since it takes 50 seconds to ride to the top on the escalator alone, we know the escalator's speed is 20m/50s = 0.4 m/s. So, when the person walks up the escalator, their speed relative to the ground is 0.5 m/s + 0.4 m/s = 0.9 m/s. To find out how long it takes for this person to reach the top, we divide the distance of 20m by their relative speed of 0.9m/s. Therefore, it will take them 20m / 0.9m/s = 22.22 seconds to get to the top. Phew, it's almost twice as fast as the escalator alone!

b) Now, let's bring some fun down to the 'up' side! When a person walks down the 'up' side of the escalator, their speed relative to the ground is the difference between their walking speed and the escalator's speed. In this case, 0.5 m/s - the speed of the escalator. Since the escalator's speed is 0.4 m/s, the person's speed relative to the ground will be 0.5 m/s - 0.4 m/s = 0.1 m/s. To find out how long it takes for this person to reach the bottom, we divide the distance of 20m by their relative speed of 0.1m/s. Therefore, it will take them 20m / 0.1m/s = 200 seconds to reach the bottom. Wow, talk about taking the scenic route!

To solve these problems, we need to consider the relative velocities of the person and the escalator.

Let's start with part (a):

a) If a person walks up the escalator at a speed of 0.5 m/s relative to the escalator, we need to find the total distance the person travels.

The person's relative speed when walking up the escalator is the sum of their walking speed and the escalator's speed. Since the escalator is moving the person up, the relative speed is the difference between their speeds.

Relative speed = Walking speed - Escalator speed

Given:
Walking speed = 0.5 m/s
Escalator speed = ? (we need to find this)

To find the escalator speed, we can divide the total distance (20 m) by the time it takes for the person to ride to the top (50 seconds).

Escalator speed = Total distance / Time
Escalator speed = 20 m / 50 s
Escalator speed = 0.4 m/s

Now that we know the escalator speed, we can calculate the time it takes for the person to get to the top.

The total distance the person needs to cover is still 20 m, but now their relative speed is the difference between their walking speed (0.5 m/s) and the escalator speed (0.4 m/s).

Relative speed = Walking speed - Escalator speed
Relative speed = 0.5 m/s - 0.4 m/s
Relative speed = 0.1 m/s

Time = Distance / Relative speed
Time = 20 m / 0.1 m/s
Time = 200 seconds

Therefore, it will take approximately 200 seconds for the person to get to the top.

Now let's move on to part (b):

b) If a person walks down the 'up' side at the same relative speed as in (a), we need to find the time it takes to arrive at the bottom.

Since the person is walking down the 'up' side, their relative speed remains the same as in part (a), which is 0.1 m/s.

Time = Distance / Relative speed
Time = 20 m / 0.1 m/s
Time = 200 seconds

Therefore, it will also take approximately 200 seconds for the person to arrive at the bottom.

So, the answers are:
a) It will take approximately 200 seconds to get to the top.
b) It will also take approximately 200 seconds to arrive at the bottom.

To answer both questions, we need to understand the concept of relative motion. Relative motion refers to the motion of an object with respect to another object or frame of reference. In these questions, we will consider the motion of the person with respect to the escalator.

a) To determine how long it takes for the person to get to the top while walking up the escalator, we need to consider the combined speeds of the person and the escalator.

Since the person is walking up the escalator at a speed of 0.5 m/s relative to the escalator, their speed with respect to the ground (or the stationary frame of reference) will be the sum of the two speeds. Therefore, the person's speed with respect to the ground is 0.5 m/s + the speed of the escalator (which we will call v).

The time it takes to travel a distance is equal to the distance divided by the speed. So, we can set up an equation:

Time = Distance / Speed

The distance is given as 20 m, and the total speed will be 0.5 m/s + v. Therefore, the time taken to reach the top is given by:

50 seconds = 20 meters / (0.5 m/s + v).

To find v, we can rearrange the equation:

v = 20 meters / 50 seconds - 0.5 m/s.

Now, we can substitute the values and calculate v:

v = 0.4 m/s.

The person's speed with respect to the ground will be 0.5 m/s + 0.4 m/s = 0.9 m/s.

Finally, we can calculate the time taken to get to the top:

Time = Distance / Speed
Time = 20 meters / 0.9 m/s
Time ≈ 22.22 seconds

Therefore, it will take approximately 22.22 seconds for the person to reach the top while walking up the escalator.

b) To determine how long it takes for the person to arrive at the bottom while walking down the 'up' side of the escalator, we need to consider the relative motion as well.

Since the person is walking down the 'up' side, their speed with respect to the ground will be the difference between their speed and the speed of the escalator.

The person's speed with respect to the ground is 0.5 m/s - v. We can set up the same equation as before:

Time = Distance / Speed

The distance is still 20 m, and the total speed will be 0.5 m/s - v. Therefore, the time taken to reach the bottom is given by:

50 seconds = 20 meters / (0.5 m/s - v).

Let's rearrange the equation to solve for v:

v = 20 meters / 50 seconds - 0.5 m/s.

Now, substitute the values and calculate v:

v = 0.4 m/s.

The person's speed with respect to the ground will be 0.5 m/s - 0.4 m/s = 0.1 m/s.

Finally, we can calculate the time taken to arrive at the bottom:

Time = Distance / Speed
Time = 20 meters / 0.1 m/s
Time = 200 seconds

Therefore, it will take 200 seconds for the person to arrive at the bottom while walking down the 'up' side of the escalator.