( ( Therefore ( if ( ( two projectiles ) ( ( start ( with ( ( ( ( ( the ( same speed ) ) , ) ( ( the first ) ( at ( angle ( with ( respect ( to ( a ( horizontal axis ) ) ) ) ) ) ) ) ) and ) ( ( the second ) ( at ( ( the angle ) ( with respect ) ) ) ) ) ) ) ( to ( vertical axis ) ) ) ) ) ) ( , ( ( their ranges ) ( ( are ( the same ) ) . ) ) ) )
(ROOT (S (SBAR (ADVP (RB Therefore)) (IN if) (S (NP (CD two) (NNS projectiles)) (VP (VBP start) (PP (IN with) (NP (NP (DT the) (JJ same) (NN speed)) (, ,) (NP (NP (DT the) (JJ first)) (PP (IN at) (NP (NP (NN angle)) (PP (IN with) (NP (NP (NN respect)) (PP (TO to) (NP (DT a) (JJ horizontal) (NNS axis)))))))) (CC and) (NP (NP (DT the) (NN second)) (PP (IN at) (NP (NP (DT the) (NN angle)) (PP (IN with) (NP (NN respect)))))))) (PP (TO to) (NP (JJ vertical) (NNS axis)))))) (, ,) (NP (PRP$ their) (NNS ranges)) (VP (VBP are) (NP (DT the) (JJ same))) (. .)))
Therefore if two projectiles start with the same speed, the first at angle with respect to a horizontal axis and the second at the angle with respect to vertical axis, their ranges are the same.
(ROOT (S (NP (NNP Range)) (VP (VBZ is) (NP (NP (DT the) (NN term)) (PP (IN for) (NP (NP (DT the) (JJ horizontal) (NN displacement)) (PP (IN of) (NP (NP (DT a) (NN projectile)) (PP (IN from) (NP (PRP$ its) (JJ starting) (NN point))))))))) (. .)))