A girl of mass 40 kg running with the velocity 2 m/s jumps on a stationary cart of mass 4 kg. Find the velocity of the girl when the cart starts moving

The problem you're describing involves the principle of conservation of momentum. The total momentum before the girl jumps on the cart should be equal to the total momentum after she jumps on the cart.

Step 1: Calculate the initial momentum of the system. The girl is moving, but the cart is stationary. So, the initial momentum (p_initial) is just the momentum of the girl, which is her mass times her velocity.

p_initial = m_girl * v_girl = 40 kg * 2 m/s = 80 kg*m/s

Step 2: After the girl jumps on the cart, they move together. The total mass is now the mass of the girl plus the mass of the cart (m_total = m_girl + m_cart = 40 kg + 4 kg = 44 kg).

Step 3: According to the conservation of momentum, the total momentum should remain the same before and after the girl jumps on the cart. So, the final momentum (p_final) should also be 80 kg*m/s.

p_final = m_total * v_total

Step 4: Solve the above equation for v_total (the velocity of the girl and the cart together after she jumps on the cart).

v_total = p_final / m_total = 80 kg*m/s / 44 kg = 1.82 m/s

So, the velocity of the girl when the cart starts moving is 1.82 m/s.