Relative Motion of a moving sidewalk

Help is much appreciated. These are extra credit problems I have.

The airport terminal has a "moving sidewalk" to speed passengers through a corridor. Peter does not use the moving sidewalk; he takes 150 s to walk through the corridor. Paul, who simply stands on the moving sidewalk, covers the same distance in 70 s. Mary boards the sidewalk and moves along it. How long does Mary take to move through the corridor? Assume that Peter and Mary walk at the same speed.

2. A person walks up a stalled 15 m long escalator in 90 s. When standing on the same escalator, now moving, the person is carried up in 60 s. How much time would it take that person to walk up the moving escalator? Does the answer depend on the length of the escalator?

3. A train travels due south at 30 m/s (relative to the ground) in a rain that is blown toward the south by the wind. The path of each raindrop makes an angle of 70 degrees with the vertical, as measured by an observer stationary on the Earth. An observer on the train, however, sees the drops fall perfectly vertically. Determine the speed of the raindrops relative to the Earth.

4. A wooden boxcar is moving along a straight railroad track at speed 85 km/h. A hunter accidentally fires a bullet (initial speed 650 km/s) from a high-powered rifle which hits it. The bullet passes through both walls of the car, its entrance and exit holes being exactly opposite each other as viewed from within the car. From what direction, relative to the track, was the bullet fired? Assume that the bullet was not deflected entering the car, but that its speed decreased by 20% (you don't need to know the width of the car to solve it!).

5. The escalators in GigantaMakk travel at a steady 0.16 m/s. The distance between floors, as measured along the escalators, is 8 m. Charlene and Dexter are at the mall going to the second floor. Both of them have a walking speed of 2 m/s.
a) Dexter simply rides the escalator to the second floor. What is tD, the time it takes him?
b) Charlene is impatient and walks up the escalator. What is her time tC?
c) On the way, Charlene decided to walk down the other escalator, re-board the upward one, and catch up to Dexter. Can she? If so, how many times can she do this before Dexter reaches the second floor? If not, how many second after Dexter does she reach the second floor (for the second time)? Assume it takes no time to switch escalators.



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