Question

Two bodies A and B, respectively with masses m1 = 2kg and m3 = 1kg, move with velocity V1 = 1 m / s and v2 = 2m / s. Marking with Ek1 and Ek2 their kinetic energies, show which of the following equations is correct and which is not, arguing your answer: 1) Ek1 = 2E2; 2) Ek1 = Ek2 / 2; 3) Ek1 = Ek2; 4) Ek1 = 4Ek2; 5) Ek1 = Ek2 / 4.

Answer 1

Find the kinetic energies:

$$E_{k1}=\frac 12 m_1v_1^2=2\text{ J}.\\\space\\ E_{k2}=\frac 12 m_2v_2^2=4\text{ J}.\\\space\\ E_{k1}=E_{k2}/2.$$