Question

question 20
a 50.0 - kg boy runs at a speed of 10.0 m/s and jumps onto a cart as shown in the figure. the cart is initially at rest. if the speed of the cart with the boy on it is 2.50 m/s, what is the mass of the cart?
210 kg
175 kg
260 kg
300 kg
150 kg

Explanation:

Step1: Apply the law of conservation of momentum

The law of conservation of momentum states that \(m_1v_1 + m_2v_2=(m_1 + m_2)v_f\). Here, \(m_1 = 50.0\space kg\), \(v_1=10.0\space m/s\), \(v_2 = 0\space m/s\) (cart is initially at rest), and \(v_f=2.50\space m/s\). Let the mass of the cart be \(m_2\).
Substituting the values into the formula: \(50\times10+ m_2\times0=(50 + m_2)\times2.5\)

Step2: Simplify the equation

The left - hand side simplifies to \(500\) (since \(m_2\times0 = 0\)). So, \(500=(50 + m_2)\times2.5\)

Step3: Solve for \(m_2\)

First, divide both sides of the equation by \(2.5\): \(\frac{500}{2.5}=50 + m_2\).
\(200=50 + m_2\)
Then, subtract \(50\) from both sides: \(m_2=200 - 50\)

Answer:

\(150\space kg\)