4. A 40kg girl is running at 3m/s on a pier from shore toward a lake. At the edge of the pier she jumps on a raft in the water. What is the speed of Jenna and the raft if the mass of the raft is 55 kg.
4. A 40kg girl is running at 3m/s on a pier from shore toward a lake. At the edge of the pier she jumps on a raft in the water. What is the speed of Jenna and the raft if the mass of the raft is 55 kg.
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![**Question:**
A 40kg girl is running at 3m/s on a pier from shore toward a lake. At the edge of the pier she jumps on a raft in the water. What is the speed of Jenna and the raft if the mass of the raft is 55 kg?
**Explanation:**
To solve this problem, we need to apply the principle of conservation of momentum. According to this principle, the total momentum before the girl jumps onto the raft will be equal to the total momentum after she lands on the raft, assuming no external forces act on the system.
**Given Data:**
- Mass of the girl (m₁) = 40 kg
- Initial velocity of the girl (v₁) = 3 m/s
- Mass of the raft (m₂) = 55 kg
- Initial velocity of the raft (v₂) = 0 m/s (since the raft is initially at rest)
**Steps to Solve:**
1. Calculate the initial momentum of the system:
\[
(\text{momentum})_{\text{initial}} = (m_1 \times v_1) + (m_2 \times v_2)
\]
Since the raft is initially at rest:
\[
(\text{momentum})_{\text{initial}} = (40 \, \text{kg} \times 3 \, \text{m/s}) + (55 \, \text{kg} \times 0 \, \text{m/s})
\]
\[
(\text{momentum})_{\text{initial}} = 120 \, \text{kg}\cdot\text{m/s}
\]
2. Let the final velocity of the girl and the raft be \( v \). According to the conservation of momentum:
\[
(\text{momentum})_{\text{final}} = (\text{total mass}) \times v
\]
The total mass is:
\[
m_{\text{total}} = m_1 + m_2 = 40 \, \text{kg} + 55 \, \text{kg} = 95 \, \text{kg}
\]
3. Set the initial momentum equal to the final momentum:
\[
120 \, \text{kg}\cdot\text{m/s} =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd34ce3f1-718c-475d-b84a-2ba4a5b1af1a%2F1c8f9e41-ebd0-45ae-a749-26443f200c0b%2Fffmmzt.png&w=3840&q=75)
Transcribed Image Text:**Question:**
A 40kg girl is running at 3m/s on a pier from shore toward a lake. At the edge of the pier she jumps on a raft in the water. What is the speed of Jenna and the raft if the mass of the raft is 55 kg?
**Explanation:**
To solve this problem, we need to apply the principle of conservation of momentum. According to this principle, the total momentum before the girl jumps onto the raft will be equal to the total momentum after she lands on the raft, assuming no external forces act on the system.
**Given Data:**
- Mass of the girl (m₁) = 40 kg
- Initial velocity of the girl (v₁) = 3 m/s
- Mass of the raft (m₂) = 55 kg
- Initial velocity of the raft (v₂) = 0 m/s (since the raft is initially at rest)
**Steps to Solve:**
1. Calculate the initial momentum of the system:
\[
(\text{momentum})_{\text{initial}} = (m_1 \times v_1) + (m_2 \times v_2)
\]
Since the raft is initially at rest:
\[
(\text{momentum})_{\text{initial}} = (40 \, \text{kg} \times 3 \, \text{m/s}) + (55 \, \text{kg} \times 0 \, \text{m/s})
\]
\[
(\text{momentum})_{\text{initial}} = 120 \, \text{kg}\cdot\text{m/s}
\]
2. Let the final velocity of the girl and the raft be \( v \). According to the conservation of momentum:
\[
(\text{momentum})_{\text{final}} = (\text{total mass}) \times v
\]
The total mass is:
\[
m_{\text{total}} = m_1 + m_2 = 40 \, \text{kg} + 55 \, \text{kg} = 95 \, \text{kg}
\]
3. Set the initial momentum equal to the final momentum:
\[
120 \, \text{kg}\cdot\text{m/s} =
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