Car collision problems

Question

Two cars collide head-on and stick together. Car A is 1,200 kg and moves east at 20 m/s. Car B is 1800 kg and moves west at 5 m/s. What is the velocity, in m/s, of the cars immediately after impact? what percentage of the kinetic energy was lost?

Answer 1

u = final velocity = ?

v_A = initial velocity of A = 20 m/s

v_B = initial velocity of B = -5 m/s

m_A = 1200 kg

m_B = 1800 kg

Conservation of linear momentum:

m_Av_A + m_Bv_B = (m_A + m_B)u

u = (m_Av_A + m_Bv_B) / (m_A + m_B)

Plug in the numbers and get u in m/s. Be careful with the signs. Negative result is west, positive result is east.

Get lost kinetic energy from

ΔK = (m_A + m_B)u²/2 - (m_Av_A²/2 + m_Bv_B²/2)

% lost is 100[ΔK / (m_Av_A²/2 + m_Bv_B²/2)].

Plug in the numbers.