Math Problem Statement
Solution
The image you've provided involves an elastic collision between two masses, with the goal of determining the final velocity of mass 1 after the collision.
The formula given is:
Where:
- (mass 1),
- (mass 2),
- (initial velocity of mass 1),
- (initial velocity of mass 2).
Step 1: Substituting values into the equation:
Step 2: Perform the calculation.
Let me compute this value for you. Given values m1 = 0.311 # kg m2 = 0.0570 # kg v1i = 30.3 # m/s v2i = -19.2 # m/s
Calculate final velocity of mass 1 using the given formula
v1f = ((m1 - m2) / (m1 + m2)) * v1i + ((2 * m2) / (m1 + m2)) * v2i v1fThe final velocity of mass 1 after the elastic collision is approximately .
Would you like any further details or clarifications?
Here are 5 related questions:
- How do you calculate the final velocity of mass 2 in an elastic collision?
- What is the principle of conservation of momentum, and how does it relate to elastic collisions?
- How do mass and velocity affect the outcome of an elastic collision?
- What are some real-world examples of elastic collisions?
- How does energy conservation apply in elastic collisions?
Tip: When solving problems with elastic collisions, always ensure that both momentum and kinetic energy are conserved!
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Math Problem Analysis
Mathematical Concepts
Elastic Collision
Momentum Conservation
Kinematics
Formulas
v_1f = ((m_1 - m_2) / (m_1 + m_2)) * v_1i + ((2 * m_2) / (m_1 + m_2)) * v_2i
Theorems
Conservation of Momentum
Elastic Collision Theorem
Suitable Grade Level
Grades 10-12
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