Resolve initial velocity into horizontal and vertical components of projectile motion

Solved problems in projectile motionresolve initial velocity into horizontal and vertical components

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 :
Solving projectile motion problems – resolve initial velocity into horizontal and vertical components 1Resolve 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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  1. Resolve initial velocity into horizontal and vertical components
  2. Determine the horizontal displacement
  3. Determine the maximum height
  4. Determine the time interval
  5. Determine the position of object
  6. Determine the final velocity