Relative Motion of a moving sidewalk

[aragornbird]

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.

Thanks!

 

[HallsofIvy]

We're not going to do your homework for you. Show us what you have tried, what formulas you have written, and where you think you are getting stuck.

 

[M98Ranger]

1. To determine the time it takes for Mary to move through the corridor, we can use the equation d = rt, where d is the distance, r is the rate (or speed), and t is the time. We know that Peter takes 150 seconds to walk through the corridor, so we can set up the equation 150 = r*t. We also know that Paul takes 70 seconds to cover the same distance while standing on the moving sidewalk, so we can set up the equation 70 = (r+v)*t, where v is the speed of the moving sidewalk. Since Peter and Mary walk at the same speed, we can set their rates equal to each other, giving us r = r+v. We can then solve for v by substituting r into the second equation, giving us 70 = (r+r)*t, which simplifies to 70 = 2r*t. We can then divide both sides by 2t to get r = 35/t. Now we can substitute this value for r into the first equation, giving us 150 = (35/t)*t. We can then solve for t by dividing both sides by 35, giving us t = 150/35 = 4.29 seconds. Therefore, it takes Mary 4.29 seconds to move through the corridor while riding on the moving sidewalk.

2. To determine the time it takes for the person to walk up the moving escalator, we can use the same equation d = rt, where d is the distance, r is the rate (or speed), and t is the time. We know that it takes 90 seconds to walk up the stalled escalator, so we can set up the equation 90 = r*t. We also know that it takes 60 seconds to be carried up the moving escalator, so we can set up the equation 60 = (r+v)*t, where v is the speed of the moving escalator. Since the distance is the same in both cases, we can set these two equations equal to each other, giving us 90 = 60 + v*t. We can then solve for v by subtracting 60 from both sides, giving us 30 = v*t. We can then substitute this value for v into the first equation, giving us 90 = 30*t. We can then solve for t by dividing both sides by 30, giving us t = 90/30