Aim: How can we determine the x (horizontal) and y (vertical) components of a vector?

Aim: How can we determine the Aim: How can we determine the x (horizontal) and y (vertical) x (horizontal) and y (vertical)

components of a vector?components of a vector?

Do Now:Do Now:

Draw a vector that is 35 m/s 30° North Draw a vector that is 35 m/s 30° North of Westof West

Scale:Scale:

1 cm = 5 m/s1 cm = 5 m/s

N

S

W E30°

35 m/s

Measure the x and y Measure the x and y componentscomponents

N

S

W E30°

35 m/s

•Draw a perpendicular line from the head of the vector to the vertical axis

•Repeat for the horizontal axis

•Measure

•Multiply by the scale (1 cm = 5 m/s)

6.1 cm

3.6 cm

= 30.5 m/s

= 18 m/s

Solving MathematicallySolving Mathematically

►Use trigonometryUse trigonometry

SOHCAHTOASOHCAHTOA

N

S

W30°

35 m/s x

y

Solving for the vertical (y) component:

hyp

oppsin

sm

y

/3530sin

)/35)(30(sin smy

smy /5.17

Solving for the horizontal (x) component:

hyp

adjcos

sm

x

/3530cos

)/35)(30(cos smx

smx /3.30

Solve both graphically and Solve both graphically and mathematicallymathematically

80 N 50° East of North80 N 50° East of North

Scale:Scale:

1 cm = 20 N1 cm = 20 N

N

S

W E

50°

80 N

N

S

W E

50°

80 N

3.1 cm

= 62 N

2.7 cm

= 54 N

Solving for the horizontal (x) component:

hyp

oppsin

N

x

8050sin

)80)(50(sin Nx

Nx 3.61

Solving for the vertical (y) component:

hyp

adjcos

N

y

8050cos

)80)(50(cos Ny

Nx 4.51

So which method of obtaining So which method of obtaining the horizontal and vertical the horizontal and vertical

components is more accurate components is more accurate and why?and why?