a person walks up a stationary escalator in t1 second if he remains stationary on the escalator then it can take him up in t2 second if the length of the escalator is L,then

1.determine the speed of man with respect to escalator
2.determine the speed of escalator
3. how much time would it take him to walk up the moving escalator?

To determine the speed of the person with respect to the escalator, we can use the formula: speed = distance / time.

1. Speed of the person with respect to the escalator:
Since the person walks up the stationary escalator in t1 seconds, the distance he covers is L. Therefore, the speed of the person with respect to the escalator is L / t1.

To determine the speed of the escalator, we need to consider that if the person remains stationary on the escalator, it takes him t2 seconds to reach the top.

2. Speed of the escalator:
As the person remains stationary on the escalator, he is carried up the length of the escalator, L, in time t2. Therefore, the speed of the escalator is L / t2.

To determine the time it would take the person to walk up the moving escalator, we need to consider their combined velocities.

3. Time it would take to walk up the moving escalator:
Let's assume that the person walks up the moving escalator with a speed of v1 (with respect to the ground) and the escalator moves with a speed of v2 (with respect to the ground).

The relative speed of the person and the escalator is v1 + v2. Therefore, the time it would take for the person to walk up the moving escalator is the distance L divided by the relative speed (v1 + v2).

Note: It is important to distinguish between the speeds of the person with respect to the escalator and the person with respect to the ground.

To answer these questions, we first need to understand the concept of relative speed.

1. The speed of the man with respect to the escalator can be determined by comparing the time it takes for him to walk up the escalator (t1) and the time it takes for the escalator to take him up (t2). Since the man is walking on the escalator, his movement is a combination of his own walking speed and the speed of the escalator.

Let's assume the man's walking speed is v and the speed of the escalator is ve.
The total distance the man covers while walking up the escalator is L (length of the escalator).
In time t1, the man walks this distance, so we can say:
Distance = Speed × Time
L = (v + ve) × t1

Now, we can calculate the speed of the man with respect to the escalator:
Speed = Distance / Time
v + ve = L / t1
v = (L / t1) - ve

2. The speed of the escalator can be determined using the previous equation by rearranging it:
Speed of escalator = Speed of man - Speed of man with respect to the escalator
ve = v - (L / t1)

3. To calculate how much time it would take him to walk up the moving escalator, we need to consider the combined speed of the man and the escalator. Let's call this combined speed v_total.
v_total = v + ve
Using this combined speed, we can calculate the time it would take the man to walk up the moving escalator, which we can call t3:
Distance = Speed × Time
L = v_total × t3
t3 = L / v_total
Substituting the value of v_total, we have:
t3 = L / (v + ve)

Finally, by substituting the values of ve (from step 2) and t3, we can get the final result for the time it would take the man to walk up the moving escalator.

if a man moves up the escalator and the escalator moves down he has, for example, Vm/g=2stair/s and the escalator has Ve/g =1stair/s, so we have resultant velocity =3stairs/s. Now, assume that as the escalator is not moving man´s Vm/g moving up is 20stairs/s. So the man´s velocity is Vm/g / 3 =20/2--> Vm/g =30stairs/s. Therefore his displacement is 30 stairs up

1) Speed of man w.r.t.escalator = L/t1

2) Speed of escalator w.r.t.ground = L/t2
3)Speed of man w.r.t.ground = (L/t1)+(L/t2)
Time taken by man to cover distance(L) = L/(L/t1)+(L/t2)
= t1*t2/(t1+t2)