Question

A 100 g ball moving to the right at 4.0 m/s collides head-on with a 200 g ball that is moving to the left at 3.0 m/s.

Answer 1

Assuming that the collision is inelastic that is they are stuck together after the collision, momentum is conserved. We can determine the final velocity of the final mass as follows:

m1v1 + m2v2 = m3v3
100(4) + (200)(-3) = (300)v3
v3 = -0.6667 m/s

Therefore, the final mass moves at 0.6667 m/s to the left.

Answer 2

The speed of the combined balls after the collision is about 0.67 m/s to the left

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Further explanation

Newton's second law of motion states that the resultant force applied to an object is directly proportional to the mass and acceleration of the object.

$\large {\boxed {F = ma }$

F = Force ( Newton )

m = Object's Mass ( kg )

a = Acceleration ( m )

Let us now tackle the problem !

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Complete Question:

A 100 g ball moving to the right at 4.0 m/s collides head-on with a 200 g ball that is moving to the left at 3.0 m/s.

If the collision is perfectly inelastic, what is the speed of the combined balls after the collision? What is the direction of the combined balls after the collision?

Given:

mass of first ball = m₁ = 100 g

mass of second ball = m₂ = 200 g

initial speed of first ball = u₁ = 4.0 m/s ( + sign means right direction )

initial speed of second ball = u₂ = -3.0 m/s ( - sign means left direction )

final speed of both balls = v₁ = v₂ = v ( perfectly inelatic collision )

Asked:

final speed of both balls = ?

Solution:

We will use Conservation of Momentum Law as follows:

$m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2$

$100(4.0) + 200(-3.0) = 100v + 200v$

$400 - 600 = 300v$

$-200 = 300 v$

$v = -200 \div 300$

$v = -\frac{2}{3} \texttt{ m/s}$

$\boxed{v \approx -0.67 \texttt{ m/s}}$

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Conclusion :

Both balls are moving to the left at about 0.67 m/s.

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Learn more

• Impacts of Gravity : https://brainly.com/question/5330244
• Effect of Earth’s Gravity on Objects : https://brainly.com/question/8844454
• The Acceleration Due To Gravity : https://brainly.com/question/4189441
• Newton's Law of Motion: https://brainly.com/question/10431582
• Example of Newton's Law: https://brainly.com/question/498822

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Answer details

Grade: High School

Subject: Physics

Chapter: Dynamics