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Transcribed Image Text:Valerie and George also join NASA to improve their transfer applications. They are doing a space walk outside the International Space Station (ISS) when the tether connecting them to it snaps and they begin to drift aimlessly in space. George remembers his Physics training and tells Valerie that if they hold each other and she throws her new iPhone 14 away from the ISS, then it will also push them towards the ISS and they would be saved. Valerie agrees, but instead pushes George away from the ISS, giving him a speed of 12 m/s. If George is 200 pounds (90.7 kg), Valerie is 115 pounds (52.2 kg), and they are both wearing 50 pound (22.7 kg) space suits, what is Valerie’s speed towards the ISS?
- ⭕ 4.9 m/s
- ⭕ 13.4 m/s
- ⭕ 18.2 m/s
- ⭕ 21.8 m/s
Explanation of the problem: This is a physics-based problem involving the conservation of momentum. By calculating the combined mass and the resulting motions after the push, we can determine Valerie's speed towards the ISS.
![**Scenario:**
Esmeralda noticed that Paige got really buff, but didn’t think she was strong enough to steal her 221-pound (100.2 kg) box of red vines so fast! Esmeralda thinks of a plan to get them back and asks their mutual friend Jailene for help. Jailene and Esmeralda go over to Paige’s place and convince her to do a Twilight marathon on Peacock. When Jailene and Paige get into a Team Edward versus Team Jacob argument, Esmeralda slips away unnoticed and starts to look for her box of red vines. Esmeralda knows that Paige keeps it in her panic room, which is two stories (25 m) underground. Because she hasn’t been to a gym since before COVID, Esmeralda isn’t strong enough to take the whole box, so decides to take half of it (50.1 kg) and needs to race up the 25 m of stairs in 15 seconds in order to make it back to Jailene and Paige before they finish their argument. If Esmeralda is 110 pounds (49.9 kg), what is the average power that her legs expend as they carry her and the half-filled box of red vines up the stairs?
**Options:**
- 654 W
- 2,512 W
- 3,190 W
- 1,633 W
**Explanation:**
To determine the average power, use the formula for power:
\[ P = \frac{W}{t} \]
where \( W \) is the work done and \( t \) is the time.
The work done \( W \) is calculated by:
\[ W = m \cdot g \cdot h \]
where:
- \( m \) is the total mass (mass of Esmeralda + mass of the half box of red vines)
- \( g \) is the acceleration due to gravity (approximately 9.8 m/s²)
- \( h \) is the height (25 meters in this scenario)
1. **Calculate the total mass:**
- Mass of Esmeralda = 49.9 kg
- Mass of half box = 50.1 kg
- Total mass = 49.9 kg + 50.1 kg = 100 kg
2. **Calculate the work done:**
\[ W = 100 \, \text{kg} \times 9.8](https://content.bartleby.com/qna-images/question/0e2724af-63d8-46e5-8bfa-efceefabbe5e/bab16213-fbf1-4f43-99da-919141cf998d/3qnqbit_processed.jpeg)
Transcribed Image Text:**Scenario:**
Esmeralda noticed that Paige got really buff, but didn’t think she was strong enough to steal her 221-pound (100.2 kg) box of red vines so fast! Esmeralda thinks of a plan to get them back and asks their mutual friend Jailene for help. Jailene and Esmeralda go over to Paige’s place and convince her to do a Twilight marathon on Peacock. When Jailene and Paige get into a Team Edward versus Team Jacob argument, Esmeralda slips away unnoticed and starts to look for her box of red vines. Esmeralda knows that Paige keeps it in her panic room, which is two stories (25 m) underground. Because she hasn’t been to a gym since before COVID, Esmeralda isn’t strong enough to take the whole box, so decides to take half of it (50.1 kg) and needs to race up the 25 m of stairs in 15 seconds in order to make it back to Jailene and Paige before they finish their argument. If Esmeralda is 110 pounds (49.9 kg), what is the average power that her legs expend as they carry her and the half-filled box of red vines up the stairs?
**Options:**
- 654 W
- 2,512 W
- 3,190 W
- 1,633 W
**Explanation:**
To determine the average power, use the formula for power:
\[ P = \frac{W}{t} \]
where \( W \) is the work done and \( t \) is the time.
The work done \( W \) is calculated by:
\[ W = m \cdot g \cdot h \]
where:
- \( m \) is the total mass (mass of Esmeralda + mass of the half box of red vines)
- \( g \) is the acceleration due to gravity (approximately 9.8 m/s²)
- \( h \) is the height (25 meters in this scenario)
1. **Calculate the total mass:**
- Mass of Esmeralda = 49.9 kg
- Mass of half box = 50.1 kg
- Total mass = 49.9 kg + 50.1 kg = 100 kg
2. **Calculate the work done:**
\[ W = 100 \, \text{kg} \times 9.8
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