we have to conserve momentum:
initial p = final p
28000kg u + 0 = (28000kg + M) v
so u = (28000 + M)v / 28000
and u² = (28000 + M)² v² / 28000²
Initial KE = ½ 28000kg u² = 14000kg u²
Final KE = ½ (28000kg + M) v² = 0.8 Initial KE = 11200kg u²
Substitute for u² and use k = 28000 for now:
½ (k + M) v² = 11200 (k + M)² v² / k² → (k + M) v² CANCELS!
½ = 11200 (k + M) / k²
k² = 22400 (k + M) = 22400k + 22400M → replace k
28000² - 22400*28000 = 22400M
M = 7000 kg
hope it helps
