Car A, with mass m_A. moves west at speed v_A while car B, with mass m_B, moves

Question

Car A, with mass m_A. moves west at speed v_A while car B, with mass m_B, moves north at speed v_B. The two cars hit each other and get stuck together. Use a reference frame with the positive x-axis pointing due-east and the positive y-axis pointing due-north: Find the velocity v vector (vector) of the two cars after the collision. Find the final combined kinetic K energy of the two cars. Find the velocity v vector_cm of the center of mass of the two cars before the collision. Show your work. Write your result in terms of m_A, v_A, m_B. and v_B. Check the units/dimensions for each answer.

Explanation / Answer

a) By law of conservation,

Pi= Pf

mA*vAi + mBvBi = mA*vAf + mBvBf

But since vAf=vBf= Vcommon

mA*vAi + mBvBi = (mA + mB)*Vcommon

Vcommon = (mA*vAi + mBvBi)/(mA + mB)

b) KEcommon = KEA+KEB= ½*(mA + mB)* Vcommon2

c) VCM = (mA*vAi + mBvB)/ (mA + mB)

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