Question

tanvi is throwing medicine balls as part of her training regimen. she throws a green medicine ball, which rolls forward at 1.4 m/s and collides with a 2 - kilogram yellow medicine ball that is at rest. after the collision, the green medicine ball continues forward at 0.5 m/s, and the yellow medicine ball rolls forward at 1.9 m/s. what is the mass of the green medicine ball? assume that friction can be ignored and that the positive direction is forward. if your answer is a decimal, round to the nearest tenth. kilograms

Explanation:

Step1: Apply the law of conservation of momentum

The law of conservation of momentum states that \(m_1u_1 + m_2u_2=m_1v_1 + m_2v_2\). Let \(m_1\) be the mass of the green ball, \(u_1 = 1.4\space m/s\), \(m_2=2\space kg\), \(u_2 = 0\space m/s\), \(v_1 = 0.5\space m/s\), \(v_2=1.9\space m/s\).
Substitute the values into the formula: \(m_1\times1.4+2\times0=m_1\times0.5 + 2\times1.9\).

Step2: Simplify the equation

The equation becomes \(1.4m_1=0.5m_1 + 3.8\).
Subtract \(0.5m_1\) from both sides: \(1.4m_1- 0.5m_1=3.8\).
So, \(0.9m_1=3.8\).

Step3: Solve for \(m_1\)

Divide both sides by \(0.9\): \(m_1=\frac{3.8}{0.9}\approx4.2\).

Answer:

\(4.2\)