Use kinematic equation Dy = (vyf^2-vyi^2)/2a to find vyi immediately after explosion. Note that of this vyi 20 m/s was due to pre explosion velocity so delta v due to explosion = vyi-20m/s = 80m/s.
impulse upward from explosion on lighter fragement = impulse downward on heavier fragment
Since other fragment was twice as massive its Dv due to the explosion is 1/2 as great so it's v right after explosion = 20 m/s( the pre-explosion v) -80/2 = -20 m/s
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