Albert is driving a 1200kg car towards east at 40m/s (90mi/hr.) approaching a red light. He collides head-on with an 800kg car driven by miss Jenny who stopped at the stoplight. a) Find the velocity of each car after the collision. a) Find the velocity of both cars together, if they are attached.
Albert is driving a 1200kg car towards east at 40m/s (90mi/hr.) approaching a red light. He collides head-on with an 800kg car driven by miss Jenny who stopped at the stoplight. a) Find the velocity of each car after the collision. a) Find the velocity of both cars together, if they are attached.
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![**Physics Problem: Collision Analysis**
**Problem Statement:**
Albert is driving a 1200 kg car towards east at 40 m/s (90 mi/hr), approaching a red light. He collides head-on with an 800 kg car driven by Miss Jenny who is stopped at the stoplight.
a) Find the velocity of each car after the collision.
b) Find the velocity of both cars together, if they are attached.
**Explanation:**
This problem involves understanding the principles of momentum and collision, typically covered in high school or introductory college-level physics courses.
To solve this problem, you may need to apply the laws of conservation of momentum and potentially conservation of energy, depending on whether the collision is elastic or inelastic.
1. **Conservation of Momentum:**
The total momentum before the collision must equal the total momentum after the collision.
\[ m_1 v_1 + m_2 v_2 = m_1 v_1' + m_2 v_2' \]
Where:
- \( m_1 \): mass of Albert's car (1200 kg)
- \( v_1 \): velocity of Albert's car before the collision (40 m/s)
- \( m_2 \): mass of Jenny's car (800 kg)
- \( v_2 \): velocity of Jenny's car before the collision (0 m/s, as it is stopped)
- \( v_1' \): velocity of Albert's car after the collision
- \( v_2' \): velocity of Jenny's car after the collision
2. **Elastic vs. Inelastic Collision:**
- **Elastic Collision**: Both momentum and kinetic energy are conserved.
- **Inelastic Collision**: Only momentum is conserved; kinetic energy is not necessarily conserved. In a perfectly inelastic collision, the cars stick together after the collision.
Given the scenario asked in part b, we are likely dealing with a perfectly inelastic collision where the cars stick together after the collision.
For part b:
Total mass after the collision: \( (m_1 + m_2) \)
Combined velocity \( V \) after collision can be found using:
\[ m_1 v_1 + m_2 v_2 = (m_1 + m_2) V \]
This problem provides a practical application of fundamental physics principles and helps students understand real-world scenarios like car collisions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd34ce3f1-718c-475d-b84a-2ba4a5b1af1a%2F2ee7f17c-7279-4c4d-9588-4cea0d80df2a%2Fxvsls1k.png&w=3840&q=75)
Transcribed Image Text:**Physics Problem: Collision Analysis**
**Problem Statement:**
Albert is driving a 1200 kg car towards east at 40 m/s (90 mi/hr), approaching a red light. He collides head-on with an 800 kg car driven by Miss Jenny who is stopped at the stoplight.
a) Find the velocity of each car after the collision.
b) Find the velocity of both cars together, if they are attached.
**Explanation:**
This problem involves understanding the principles of momentum and collision, typically covered in high school or introductory college-level physics courses.
To solve this problem, you may need to apply the laws of conservation of momentum and potentially conservation of energy, depending on whether the collision is elastic or inelastic.
1. **Conservation of Momentum:**
The total momentum before the collision must equal the total momentum after the collision.
\[ m_1 v_1 + m_2 v_2 = m_1 v_1' + m_2 v_2' \]
Where:
- \( m_1 \): mass of Albert's car (1200 kg)
- \( v_1 \): velocity of Albert's car before the collision (40 m/s)
- \( m_2 \): mass of Jenny's car (800 kg)
- \( v_2 \): velocity of Jenny's car before the collision (0 m/s, as it is stopped)
- \( v_1' \): velocity of Albert's car after the collision
- \( v_2' \): velocity of Jenny's car after the collision
2. **Elastic vs. Inelastic Collision:**
- **Elastic Collision**: Both momentum and kinetic energy are conserved.
- **Inelastic Collision**: Only momentum is conserved; kinetic energy is not necessarily conserved. In a perfectly inelastic collision, the cars stick together after the collision.
Given the scenario asked in part b, we are likely dealing with a perfectly inelastic collision where the cars stick together after the collision.
For part b:
Total mass after the collision: \( (m_1 + m_2) \)
Combined velocity \( V \) after collision can be found using:
\[ m_1 v_1 + m_2 v_2 = (m_1 + m_2) V \]
This problem provides a practical application of fundamental physics principles and helps students understand real-world scenarios like car collisions.
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