= Solution
For an <elastic collision> with $M_2>M_1$, the positive root in the <laboratory scattering circle> formula is the only nonnegative one. With $\varepsilon=M_1/M_2\ll1$,
$$
\frac{v_1}{u_1}
=\frac{\varepsilon\cos\theta_1+\sqrt{1-\varepsilon^2\sin^2\theta_1}}{1+\varepsilon}
=1-\varepsilon(1-\cos\theta_1)+O(\varepsilon^2).
$$
Consequently
$$
\boxed{v_1\longrightarrow u_1\quad\text{as }M_2/M_1\to\infty.}
$$
The heavy target can absorb a finite <momentum> with negligible <velocity> and negligible <kinetic energy>. Thus the projectile may change direction substantially while retaining its <speed>; a backward reflection also has $v_1\simeq u_1$.
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