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

Solved problems in projectile motion – resolve initial velocity into horizontal and vertical components

1. A kicked football leaves the ground at an angle θ = 60^{o} with a velocity of 10 m/s. Calculate the initial velocity components!

Known :

Angle (θ) = 60^{o}

Initial velocity (v_{o}) = 10 m/s

Wanted : v_{ox} dan v_{oy}

Solution :

Resolve the initial velocity into x component (horizontal) and y component (vertical).

sin θ = v_{oy} / v_{o} —–> v_{oy} = v_{o} sin θ

cos θ = v_{ox} / v_{o} —–> v_{ox} = v_{o} cos θ

x component (horizontal) :

v_{ox} = v_{o} cos θ = (10 m/s)(cos 60^{o}) = (10 m/s)(0.5) = 5 m/s

y component (vertical) :

v_{oy} = v_{o} sin θ = (10 m/s)(sin 60^{o}) = (10 m/s)(0.5√3) = 5√3 m/s

2. An object leaves ground at an angle θ = 30^{o} with y component of the velocity 10 m/s. Calculate initial velocity !

Known :

Angle (θ) = 30^{o}

y component (v_{oy}) = 10 m/s

Wanted : Initial velocity (v_{o})

Solution :

v_{oy} = v_{o} sin θ

10 = (v_{o})(sin 30^{o})

10 = (v_{o})(0.5)

v_{o} = 10 / 0.5

v_{o} = 20 m/s

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 (v_{ox}) = 30 m/s

Vertical component of initial velocity (v_{oy}) = 40 m/s

Wanted : Initial velocity (v_{o})

Solution :

v_{o}^{2} = v_{ox}^{2} + v_{oy}^{2} = 30^{2} + 40^{2} = 900 + 1600 = 2500

v_{o} = √2500

v_{o} = 50 m/s

4. A small ball projected horizontally with initial velocity v_{o} = 6 m/s. Calculate x component and y component of initial velocity.

Known :

Initial velocity (v_{o}) = 6 m/s

Wanted : vox and v_{oy}

Solution :

Ball move horizontally so that horizontal component of velocity (v_{ox}) = initial velocity (v_{o}) = 6 m/s. Vertical component of velocity (v_{oy}) = 0.

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- Resolve initial velocity into horizontal and vertical components
- Determine the horizontal displacement
- Determine the maximum height
- Determine the time interval
- Determine the position of object
- Determine the final velocity