( ( ( Applying ( conservation ( of ( linear momentum ) ) ) ) ( to ( ( the collision ) ( shown ( in ( Figure 10.1 ) ) ) ) ) ) ( ( gives ( ( Conservation ( of ( the ( total ( kinetic energy ) ) ) ) ) ( gives ( We ( now ( have ( ( two equations ) ( with ( ( ( two unknown ) ( -LRB- ( ( ( ( v 1f ) and ) ( v 2f ) ) -RRB- ) ) ) ( which ( can ( be solved ) ) ) ) ) ) ) ) ) ) ) ) . ) )
(ROOT (S (S (VP (VBG Applying) (NP (NP (NN conservation)) (PP (IN of) (NP (JJ linear) (NN momentum)))) (PP (TO to) (NP (NP (DT the) (NN collision)) (VP (VBN shown) (PP (IN in) (NP (NNP Figure) (CD 10.1)))))))) (VP (VBZ gives) (SBAR (S (NP (NP (NNP Conservation)) (PP (IN of) (NP (DT the) (JJ total) (JJ kinetic) (NN energy)))) (VP (VBZ gives) (SBAR (S (NP (PRP We)) (ADVP (RB now)) (VP (VBP have) (NP (NP (CD two) (NNS equations)) (PP (IN with) (NP (NP (CD two) (NN unknown)) (PRN (-LRB- -LRB-) (NP (NP (NN v) (NNS 1f)) (CC and) (NP (NN v) (NNS 2f))) (-RRB- -RRB-)) (SBAR (WHNP (WDT which)) (S (VP (MD can) (VP (VB be) (VP (VBN solved)))))))))))))))) (. .)))
Applying conservation of linear momentum to the collision shown in Figure 10.1 gives Conservation of the total kinetic energy gives We now have two equations with two unknown (v 1f and v 2f ) which can be solved.
(ROOT (S (NP (DT A) (ADJP (RB perfectly) (JJ inelastic)) (NN collision)) (VP (VBZ reduces) (NP (JJ internal) (JJ kinetic) (NN energy)) (PP (TO to) (NP (NP (DT the) (NN minimum)) (SBAR (S (NP (PRP it)) (VP (MD can) (VP (VB have) (NP (NN while)) (ADVP (RB still)) (S (VP (VBG conserving) (NP (NN momentum))))))))))) (. .)))