( ( Since ( impulse ( equals ( ( ( ( a change ) ( in momentum ) ) and ) ( since ( ( the ( two objects ) ) ( have ( equal ( and ( opposite impulses ) ) ) ) ) ) ) ) ) ) ( , ( they ( ( ( must also ) ( have ( ( equal ( and ( opposite changes ) ) ) ( in momentum ) ) ) ) . ) ) ) )
(ROOT (S (SBAR (IN Since) (S (NP (NN impulse)) (VP (VBZ equals) (UCP (NP (NP (DT a) (NN change)) (PP (IN in) (NP (NN momentum)))) (CC and) (SBAR (IN since) (S (NP (DT the) (CD two) (NNS objects)) (VP (VBP have) (NP (JJ equal) (CC and) (JJ opposite) (NNS impulses))))))))) (, ,) (NP (PRP they)) (VP (MD must) (ADVP (RB also)) (VP (VB have) (NP (NP (JJ equal) (CC and) (JJ opposite) (NNS changes)) (PP (IN in) (NP (NN momentum)))))) (. .)))
Since impulse equals a change in momentum and since the two objects have equal and opposite impulses, they must also have equal and opposite changes in momentum.
(ROOT (S (NP (NP (NNP Change)) (PP (IN in) (NP (NP (NN momentum)) (PP (IN in) (NP (DT an) (NN object)))))) (VP (VBZ is) (ADJP (JJ equivalent) (PP (TO to) (NP (NN impulse))))) (. .)))