A block of mass ${?}_1=1\mathrm{.}50??$ ?moving at ${?}_1=2\mathrm{.}00\frac{?}{?}$ ?undergoes a completely inelastic collision with a stationary block of mass ${?}_2=0\mathrm{.}600$ $??.$ ?The blocks then move, stuck together, at speed ${?}_2.$ ?After a short time, the two$-$block system collides inelastically with a third block, of mass ${?}_3=$ $3\mathrm{.}00??,$ ?which is initially at rest. The three blocks then move, stuck together, with speed ${?}_3.($Figure $1)$ ?Assume that the blocks slide without friction.

Part A Find $\frac{{?}_2}{{?}_1},$ ?the ratio of the velocity ${?}_2$ ?of the two$-$block system after the first collision to the velocity ${?}_1$ ?of the block of mass ${?}_1$ ?before the collision.

Express your answer numerically using three significant figures.

Figure mi m2 m3 m3 m m2 m3 m1 m2 1 of 1