Misali na tambaya don tantance abubuwan da suka fara saurin motsi na parabolic

4 Misalan tambayoyi don tantance abubuwan da suka shafi saurin farko na motsi na parabolic

1. An buga ƙwallon a kusurwar 60^o a saman filin. Idan saurin farko (v)_o) 10 m/s, ƙayyade sassan tsaye da kwance gudun ƙwallon farko!
Tattaunawa
An san cewa:
Kusurwoyi (θ) = 60^o
Saurin farko (v)_o) = 10 m/s
An tambaya: v_ox kuma v_oy
Amsa:

zunubi θ = v_oy /v_o —–> v_oy = v_o zunubi θ
cos θ = v_ox /v_o —–> v_ox = v_o kowa

Sashen kwance na saurin farko na ƙwallon:
v_ox = v_o cos θ = (10 m/s)(cos 60^o) = (10 m/s)(0,5) = 5 m/s

Bangaren tsaye na saurin farko na ƙwallon:
v_oy = v_o zunubi θ = (10 m/s)(zunubi 60^o) = (10 m/s)(0,5√3) = 5√3 m/s

2. Ana jefa wani abu sama a kusurwar 30°^o zuwa kwance. Idan bangaren tsaye na saurin abu (v)_oy) shine 10 m/s, ƙididdige saurin farko na abu (v_o)!
Tattaunawa
An san cewa:
Kusurwoyi (θ) = 30^o
Bangaren tsaye na saurin farko (v)_oy) = 10 m/s
An tambaya: Saurin farko na abu (v)_o)
Amsa:
Tsarin da aka yi amfani da shi don ɓangaren tsaye na saurin farko:
v_oy = v_o zunubi θ
10 = (v_o) (zunubi 30^o)
10 = (v_o(0,5)
v_o = 10/0,5
v_o = 20m/s
Saurin farko na abu shine 20 m/s.

3. Sashen kwance na saurin harsashin shine m30/s kuma sashin tsaye na saurin harsashin shine m40/s. Menene saurin harsashin farko?
Tattaunawa
An san cewa:
Sashen kwance na saurin harsashi (v)_ox) = 30 m/s
Bangaren tsaye na saurin harsashi (v)_oy) = 40 m/s
An tambaya: Saurin farko na harsashi (v)_o)
Amsa:
Ana ƙididdige saurin farko na harsashi ta amfani da dabarar Pythagorean:
v_o² = v_ox² +v_oy² = 30² + 40² = 900 + 1600 = 2500
v_o = √2500
v_o = 50m/s
Saurin farko na harsashi shine 50 m/s.

4. Ana jefa marmara a kwance zuwa dama daga ginin hawa da yawa. Idan saurin farko na marmara shine m6/s, menene saurin farko na marmara a cikin kwatancen kwance da tsaye?
Tattaunawa
An san cewa:
Saurin farko na marmara (v)_o) = 6 m/s
An tambaya: Saurin farko na marmara a cikin shugabanci na kwance (v)_ox) da kuma tsaye (v_oy)
Amsa:
Hanyar marmara tana kama da hoton.
Da farko, marmarar tana motsawa a kwance ta yadda saurin farko na marmarar a kwance (v)_ox) = saurin farko na marmara (v_o) = 6 m/s.
A halin yanzu, saurin farko na marmara a tsaye shine sifili.

[Turanci: Magance matsalolin motsin harsashi - Magance saurin farko zuwa sassan kwance da tsaye ]