The metro passenger who got on the escalator got off it through t (s). Descent depth h (m)

The metro passenger who got on the escalator got off it through t (s). Descent depth h (m) The angle of the escalator to the horizontal plane is 30 degrees. Express by the formula the dependence of h on t, if the speed of the escalator is 0.75 m / s. Find a) h. if t = 2.25 MIN b) t, If h = 60 m

We express the length of the escalator span from a right-angled triangle:
L = h / sin 30 ° = 2 * h

Let us find the time for which moving at a speed of 0.75 m / s the escalator travels the path L
t = L / 0.75 = 2 * h / 0.75 = 8 * h / 3.

h = t * 3/8

a) If t = 2.25 min = 135 s, then the descent depth
h = 3 * 135/8 = 50.635 m.

b) If h = 60 m, then the descent time
t = 8 * 60/3 = 160 s = 2 min 40 s.