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_o² = v_ox² + v_oy² = 30² + 40² = 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.

[wpdm_package id=’545′]

[wpdm_package id=’536′]

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