Dane:
y=100m
x=400m
Szukane:
α=?
Rozwiązanie:
y(t)=Vyt-(gt²/2)
Vy=(2y+gt²)/2t
x(t)=Vxt
Vx=x/t
t=Vy/g
Vy=(2y+gt²)/2t
y=gt²/2
t=√(2y/g)
t=√100m/10m/s²=√10
Vy/Vx = tg α
tg α =[(2y+gt²)/2t]/[x/t]=(2y+gt²)/2t*t/x = (2y+gt²)/2x
tg α =(2y+gt²)/2x = 200m+10m/s²*(√10s)²/800m
tg α = 200m+100m/800m=3/8
α = arctg 3/8
arctg 3/8 =~ 20.56°
Odpowiedź:
Kąt α wynosi 20,56°.
