A 2 kg lump of red Playfough moving at 35 m/s hits a stationary 5kg lump of yellow Playdough. How fast will the resulting lump of orange playdough be moving?

Answer 1

Let's assume that when they say red Playfough hits yellow Playdough and results in orange playdough means the two stick together into one lump.

Let's let v_r and m_r be the velocity and mass of the red, v_y and my be the velocity and mass of the yellow, and v_o and m_o be the velocity and mass of the orange. Let's also let time 1 be the time when the red is moving and yellow is still and let time 2 be when the red/yellow are combined and that "orange": is moving. That makes m_r = 2, v_r1 = 35, m_y = 5, and v_y1 = 0

The conservation of momentum says that for an isolated system, the total momentum (P) at any point in time is conserved (the same).

So at time t = 1, the total momentum is m_r*v_r1 + m_y*v_y1 = 2*35 + 5*0 = 70 kg*m/s

At time 2, the total momentum is m_o*v_o2. Also, we know that m_o = m_r + m_y = 2 + 5 = 7 kg

So, since P1 = P2, then 70 = m_o*v_o2 = 7*v_o2 so v_o2 = 70/7 = 10 m/s