Projectile Motion. Parabolic Motion curved motion in the shape of a parabola. In the y direction, the equation of motion has a t 2.

Transcription

1 Projectle Moton Phc Inentor Parabolc Moton cured oton n the hape of a parabola. In the drecton, the equaton of oton ha a t ter Projectle Moton the parabolc oton of an object, where the horzontal coponent rean contant and the ertcal oton chane wth te. Rane the dtance a projectle trael n the horzontal drecton. Intal Veloct Anle the anle of a projectle oton, eaured relate to the horzontal unle otherwe tated. Dtance Equaton: drecton: d t where 1 co drecton: d t 4.9 t where n Rane Equaton: for an object that land at the ae heht at whch t tart n d and n t Mau Heht: for an object that land at the ae heht at whch t tart h n and t n The horzontal rane R a au for a launch anle of 45. Projectle oton the cobnaton of two tpe of kneatc proble: one noln acceleraton due to rat, and the other noln a contant eloct n one drecton. In projectle oton, the horzontal oton and the ertcal oton are ndependent of each other; that, nether oton affect the other. Note: We hae aued that the ar throuh whch the projectle oe ha no effect on t oton. Howeer, n an tuaton, the dareeent between our calculaton and the actual oton of the projectle can be lare becaue the ar ret the oton. Step for Soln Projectle Moton Proble 1. Denate a n conenton for drecton. Mot proble ue + for oton that ether upward or to the rht. In cae where the object alwa falln, ou a fnd t adantaeou to denate + for downward oton.. Separate the en alue nto ther horzontal () and ertcal coponent () 3. Wrte down the correpondn equaton for each coponent. 4. If ou can calculate TIME n ether the or drecton then do o, and the ue our anwer to calculate the rane or heht.

2 5. If the equaton n the and drecton each hae two unknown alue then ue the ubttuton ethod to ole. Note: The horzontal ntal eloct ean that 0. If the projectle land at the ae heht t tarted fro, then d 0. Once the object leae the table, t eperence a downward acceleraton equal to rat. Thu the ertcal eloct( ) contnuall ncrean. The horzontal eloct( ) rean contant and equal to. The two ector eloct at each pont on the path. and are added toether to et the If an object ponted at an anle, the oton eentall the ae ecept that there now an ntal ertcal eloct ( ). Becaue of the downward acceleraton of rat, contnuall decreae untl t reache t hhet pont, at whch t ben to fall downward.

3 Eaple: A baeball thrown wth an ntal horzontal eloct of 85 / at an anle of 50 aboe the horzontal. How far doe the baeball trael? Soluton: We are en 85, 50,? We wll denate the pote drecton a to the rht and upward. d Now d t co t 85 co50 t t We need t, whch wll coe fro the horzontal coponent to the flht. Un d t 4.9t n t 4.9 t 85 n t 4.9 t t t Soln wth the quadratc forula t b b 4ac a Subttutn th nto d t nfcant dt

4 Eaple A ball toe fro the top of a cence buldn wth a horzontal eloct coponent of 15 / [rht] and a ertcal coponent of 0 / [up]. If the roof wa 100 hh, how far wll the ball trael? Soluton: We are en: 15, 0 Let frt fnd the te for the trp fro the horzontal coponent. d t 4.9 t t 4.9 t 4.9 t 0t100 0 d Now un the quadratc forula to ole for t b b 4ac a or.9 t.

5 Snce a neate te poble n real lfe, the correct te 7.0. To deterne the rane, we ubttute th alue nto The ball trael 105 d t Eaple A ball roll of a lanted roof (lant 30 wth repect to the horzontal). The ball rolln wth a peed of 4.1 / fall 6.0 etre to the round. a) how lon wa the ball n the ar after t left the roof? b) at what wa the horzontal dtance fro the roof dd the ball ht the round? c) What wa the pact peed of the ball? Soluton: a) Fro d t 4.9t 6 4.1n 30 t 4.9 t 4.9 t.05 t 6 0 Fro the quadratc forula t b b 4ac a or Therefore the ball took 0.9 econd to ht the round b) Fro d t 4.1 co

6 c) We wll chooe down to be pote Fro a t f co 30 Unque Forula Un f at for ertcal drecton we obtan to te for an object that launche at the ae alttude to arre back down at the ae alttude [rane te]: n n t n at f t n t Therefore, t take half of th te to reach the au heht: t n We can ubttute th alue nto 1 t at to deterne forula for au heht. n 1 n h n n

7 For rane, we ue: d t n co n co n

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