Questions: Question 7 12 pts 7. Relative Motion. As you hurry to catch a flight at the local airport, you encounter a moving walkway that is 85 m long and moving with a speed of 2.2 m / s relative to the ground. If it takes 68 s to cover 85 m when walking on the ground, [Note: W - Walkway: P = Passenger; G = Ground] 1. Determine (a) vWG. (b) vPW, (c) vPG. Solution: (a) vWG= 2.2 m / s (b) vPW= -0.95 m / s (c) vPG= 1.3 m / s II. How long will it take you to cover the same distance on the walkway if you walk with the same speed as you walk on the ground? Solution: t= 25 s III. How long will it take to cover the 85-m length of the walkway if a traveler walked in the opposite direction on the moving walkway with a speed of 1.3 m / s relative to the walkway? Determine the traveler's velocity relative to the ground. Solution: Time: 94 s Velocity: vTG=0.9 m / s

Question 7 12 pts 7. Relative Motion. As you hurry to catch a flight at the local airport, you encounter a moving walkway that is 85 m long and moving with a speed of 2.2 m / s relative to the ground. If it takes 68 s to cover 85 m when walking on the ground, [Note: W - Walkway: P = Passenger; G = Ground] 1. Determine (a) vWG. (b) vPW, (c) vPG. Solution: (a) vWG= 2.2 m / s (b) vPW= -0.95 m / s (c) vPG= 1.3 m / s II. How long will it take you to cover the same distance on the walkway if you walk with the same speed as you walk on the ground? Solution: t= 25 s III. How long will it take to cover the 85-m length of the walkway if a traveler walked in the opposite direction on the moving walkway with a speed of 1.3 m / s relative to the walkway? Determine the traveler's velocity relative to the ground. Solution: Time: 94 s Velocity: vTG=0.9 m / s
Transcript text: Question 7 12 pts 7. Relative Motion. As you hurry to catch a flight at the local airport, you encounter a moving walkway that is 85 m long and moving with a speed of $2.2 \mathrm{~m} / \mathrm{s}$ relative to the ground. If it takes 68 s to cover 85 m when walking on the ground, [Note: W - Walkway: P = Passenger; G = Ground] 1. Determine (a) $\vec{v}_{W G}$. (b) $\vec{v}_{P W}$, $\quad$ (c) $\vec{v}_{P G}$. Solution: (a) $\vec{v}_{W G}=$ $2.2 \mathrm{~m} / \mathrm{s}$ (b) $\vec{v}_{P W}=$ $-0.95 \mathrm{~m} / \mathrm{s}$ (c) $\vec{v}_{P G}=$ $1.3 \mathrm{~m} / \mathrm{s}$ II. How long will it take you to cover the same distance on the walkway if you walk with the same speed as you walk on the ground? Solution: $t=$ 25 s III. How long will it take to cover the $85-\mathrm{m}$ length of the walkway if a traveler walked in the opposite direction on the moving walkway with a speed of $1.3 \mathrm{~m} / \mathrm{s}$ relative to the walkway? Determine the traveler's velocity relative to the ground. Solution: Time: 94 s \[ \text { Velocity: } \vec{v}_{T G}=0.9 \mathrm{~m} / \mathrm{s} \]
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Solution

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Solution Steps

Step 1: Determine \(\vec{v}_{W G}\)
  • The velocity of the walkway relative to the ground, \(\vec{v}_{W G}\), is given directly in the problem statement as \(2.2 \, \mathrm{m/s}\).
Step 2: Calculate \(\vec{v}_{P W}\)
  • The passenger's speed on the ground is calculated by dividing the distance by the time: \[ \vec{v}_{P G} = \frac{85 \, \mathrm{m}}{68 \, \mathrm{s}} = 1.25 \, \mathrm{m/s} \]
  • The velocity of the passenger relative to the walkway, \(\vec{v}_{P W}\), is given as \(-0.95 \, \mathrm{m/s}\).
Step 3: Calculate \(\vec{v}_{P G}\)
  • The velocity of the passenger relative to the ground, \(\vec{v}_{P G}\), is the sum of the passenger's velocity relative to the walkway and the walkway's velocity relative to the ground: \[ \vec{v}_{P G} = \vec{v}_{P W} + \vec{v}_{W G} = -0.95 \, \mathrm{m/s} + 2.2 \, \mathrm{m/s} = 1.25 \, \mathrm{m/s} \]

Final Answer

(a) \( \vec{v}_{W G} = \boxed{2.2 \, \mathrm{m/s}} \)(b) \( \vec{v}_{P W} = \boxed{-0.95 \, \mathrm{m/s}} \)
(c) \( \vec{v}_{P G} = \boxed{1.25 \, \mathrm{m/s}} \)II. \( t = \boxed{25 \, \mathrm{s}} \)III. Time: \( \boxed{94 \, \mathrm{s}} \)Velocity: \( \vec{v}_{T G} = \boxed{0.9 \, \mathrm{m/s}} \)

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