The initial speed of the 1.00 kg block is approximately 8.94 m/s. since the final velocity are the same since they stick together
m1 = 1.00 kg (mass of the 1.00 kg block)
m2 = 5.00 kg (mass of the 5.00 kg block)
KE_initial = 32.0 J (initial kinetic energy)
v1_initial (unknown) = initial speed of the 1.00 kg block
v_final = final speed of both blocks after the collision
v1_initial² = (KE_initial * m2) / (m1 * (m1 + m2))
v1_initial = √t((32.0 J * 5.00 kg) / (1.00 kg * (1.00 kg + 5.00 kg)))
v1_initial = 8.94 m/s
complete question:
Two blocks of clay, one of mass 1.00 kg and one of mass 5.00 kg , undergo a completely inelastic collision. before the collision one of the blocks is at rest and the other block is moving with kinetic energy 32.0 j . if the 5.00 kg block is initially at rest and the 1.00 kg block is moving, what is the initial speed of the 1.00 kg block? express your answer with the appropriate units.