Question

A passenger rushing to catch a plane at the airport walks on a moving sidewalk at a speed of 3.5 km/h relative to the sidewalk in the direction that the sidewalk is moving. The sidewalk is 105 m long and moves with a steady velocity of 1.9 km/h.

How much time does the passenger save by taking the moving sidewalk instead of just walking beside it?

Through what distance does the passenger walk relative to the moving sidewalk?

If the passenger's stride is 80 cm, how many steps are taken in going from one end of the moving sidewalk to the other?

Answer 1

speed of side walk vsE = 1.9 km/h

speed of passenger vps = 3.5 km/h

speed of passenger relative to earth vpE = Vps + VsE = 1.9 + 3.5 = 5.4 km/h

time taken by side walk t1 = d/vsE =

time taken by passenger t2 = d/vPE

time saved = t1 - t2 = d*(1/vsE - 1/VPE)

t1 - t2 = 105*10^-3*(1/1.9 - 1/5.4)

t1 - t2 = 0.0358 hour

t1 - t2 = 0.0358*60 minutes

time saved t1 - t2 = 2.15 minutes

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dPs = dPE + dEs

dPs = dPE - dsE

dPs = dPE - VSE*t2

dPs = dPE - VsE*d/VpE

dPs = 0.105 - 1.9*0.105/5.4 = 0.068 km = 68 m

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length of each step L = 0.8 m

number of steps N = dPs/L = 68/0.8 = 85 steps