Skrått kast

[mathia1808]

Hei! Trenger litt starthjelp på dette området. Vi har gjort et forsøk hvor vi skjøt en liten gjenstand ut fra en katapult. Vi fikk disse resultatene: Lengde =5,83 m, Høyde=1,85 m, Utgangsvinkel= 45 grader, og tid 1,67 s. Hele oppgaven går ut på å finne startfarten v0. Noen som har noen forslag?

Takk

[mbe]

Det er dessverre nesten umulig å skrive noe annet en ren tekst i dette forumet, men her er et forsøk på en liten starthjelp.
Siden vinkelen var 45 grader var komponentene av starthastigheten i horisontal- og vertikalretningene numerisk like. Dere har mer enn nok data til å finne startfarten når en ser bort fra luftmotstand.
Basert på horisontalkomponenten som er den samme hele tida: v0h = sh/t = (5,83/1,67) m/s = 3,49 m/s
Basert på vertikalkomponenten ver.1 . v0v = sqrt(2hg) m/s =sqrt (3,70*9,81) m/s = 6,02 m/s
Basert på vertikalkomponenten ver.2 v0v = 9,81*1,67/2 m/s = 8,19 m/s

Det var store variasjoner noe som tyder på store målefeil. For et skrått kast på 45 grader er: lengde/høyde = 4. Her er det 5,83/1,85 = 3,15

Litt mer analyse: Vi antar at kastlengden er den "beste" målingen.
Et slikt kast på 5,83m krever en hastighet på v0 =sqrt(gs) = sqrt (9,81*5,83) m/s = 7,56 m/s
Horisontalkomponenten 7,56/sqrt(2) m/s 5,35 m/s
Tida: (5,83*sqrt(2)/7,56)s = 1.09 s
Det tyder i alle fall på grove feil i tidsmålingen dersom kastvinkelen virkelig var 45 grader!
Høyden er: (5,83/4) m = 1,46m. Her er det også betydelig avvik.
Basert på "rådata" burde kastvinkelen være ca: Arctg(6,02/3,49) ~ 60 grader

Forbehold for regnefeil.
Sett under ett er det rimelig å anta at kastvinkelen var noe større enn 45 grader.

[LucyHonle]

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