  We present Magellan/IMACS spectroscopy of three recently discovered
ultra-faint Milky Way satellites, Grus II, Tucana IV, and Tucana V. We measure
systemic velocities of V_hel = -110.0 +/- 0.5 km/s, V_hel = 15.9 +/- 1.8 km/s,
and V_hel = -36.2 +/-2.5 km/s for the three objects, respectively. Their large
relative velocity differences demonstrate that the satellites are unrelated
despite their close physical proximity. We determine a velocity dispersion for
Tuc IV of sigma = 4.3^+1.7_-1.0 km/s, but we cannot resolve the velocity
dispersions of the other two systems. For Gru II we place an upper limit (90%
confidence) on the dispersion of sigma < 1.9 km/s, and for Tuc V we do not
obtain any useful limits. All three satellites have metallicities below [Fe/H]
= -2.1, but none has a detectable metallicity spread. We determine proper
motions for each satellite based on Gaia astrometry and compute their orbits
around the Milky Way. Gru II is on a tightly bound orbit with a pericenter of
25 kpc and orbital eccentricity of 0.45. Tuc V likely has an apocenter beyond
100 kpc, and could be approaching the Milky Way for the first time. The current
orbit of Tuc IV is similar to that of Gru II, with a pericenter of 25 kpc and
an eccentricity of 0.36. However, a backward integration of the position of Tuc
IV demonstrates that it collided with the Large Magellanic Cloud at an impact
parameter of 4 kpc ~120 Myr ago, deflecting its trajectory and possibly
altering its internal kinematics. Based on their sizes, masses, and
metallicities, we classify Gru II and Tuc IV as likely dwarf galaxies, but the
nature of Tuc V remains uncertain.
