# Resolve initial velocity into horizontal and vertical components of projectile motion

1. A kicked football leaves the ground at an angle θ = 60o with a velocity of 10 m/s. Calculate the initial velocity components!
Known :
Angle (θ) = 60o
Initial velocity (vo) = 10 m/s
Wanted : vox dan voy
Solution : Resolve the initial velocity into x component (horizontal) and y component (vertical).
sin θ = voy / vo —–> voy = vo sin θ
cos θ = vox / vo —–> vox = vo cos θ

x component (horizontal) :
vox = vo cos θ = (10 m/s)(cos 60o) = (10 m/s)(0.5) = 5 m/s

y component (vertical) :
voy = vo sin θ = (10 m/s)(sin 60o) = (10 m/s)(0.5√3) = 5√3 m/s

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2. An object leaves ground at an angle θ = 30o with y component of the velocity 10 m/s. Calculate initial velocity !
Known :
Angle (θ) = 30o
y component (voy) = 10 m/s
Wanted : Initial velocity (vo)
Solution :
voy = vo sin θ
10 = (vo)(sin 30o)
10 = (vo)(0.5)
vo = 10 / 0.5
vo = 20 m/s

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3. Horizontal component of initial velocity is 30 m/s and vertical component of initial velocity is 40 m/s. Calculate initial velocity.
Known :
Horizontal component of initial velocity (vox) = 30 m/s
Vertical component of initial velocity (voy) = 40 m/s
Wanted : Initial velocity (vo)
Solution :
vo2 = vox2 + voy2 = 302 + 402 = 900 + 1600 = 2500
vo = √2500
vo = 50 m/s

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4. A small ball projected horizontally with initial velocity vo = 6 m/s. Calculate x component and y component of initial velocity.
Known :
Initial velocity (vo) = 6 m/s
Wanted : vox and voy
Solution :
Ball move horizontally so that horizontal component of velocity (vox) = initial velocity (vo) = 6 m/s. Vertical component of velocity (voy) = 0.

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