Physics Chp 3

Trig Functionscos(θ) = x/h or =a/hsin(θ) =y/h or =o/htan(θ) =y/x or =o/a

soh cah toa

θ

y

x

H or R R is the resultant

scalars vs vectors vectors have a value and direction resultant is the combination of vectors. We can

add parallel vectors and we can break a vector into x and y components then adding them and calculating the resultant.

• R2 = x2 +y2 R = • • tan(θ) = y/x θ=

• If x = 3 and y = 2 find R •

• R2 = 32 +22 R =

• tan(θ) = 2/3 θ= tan-1(2/3) =

• What about this?

θ

11

8

R =? R is the resultant

• Still R2 = 112 + 82 R =

tan(θ) = 8/11 θ= tan-1(8/11) =

We use the same equations for 2 dimensions as we did for one. Just label them x or y

vx = vox +axΔt

Δx = 1/2(vo + vx)Δt

Δx = voxΔt + 1/2ax(Δt)2

vx

2 = vox2 + 2axΔx

vy = voy +ayΔt Δy = 1/2(vo + vy)Δt Δy = voyΔt + 1/2ay(Δt)2

vy

2 = voy2 + 2ayΔy

• Ex How long does it take a ball kicked off a 45 m tall building to hit the ground?

• voy = 0 y= -45m ay= -9.8 m/s2 t = ?

Δy = voyΔt + 1/2ay(Δt)2

-45m = 0 + ½(-9.8m/s2)(Δt)2

t =

How far away from the building would the ball hit if you kicked it with a velocity of 5.4 m/s horizontally?

vox = 5.4 m/s ∆t = 3.0s ax = 0 ∆x =?

Δx = 1/2(vo + vx)Δt OR Δx = voxΔt + 1/2ax(Δt)2

Δx = 5.4 m/s (3.0s) + ½ (0)(3.0s)2

EX. If a dog jumps from a dock with an initial velocity of 3.4 m/s at 15o above the horizontal, how high does the dog go?

vo = 3.4 m/s θ = 15o ∆y= ?

vox = 3.4m/s cos15o = 3.3 m/s

ax = 0

voy = 3.4m/s sin15o = 0.88 m/s

ay = - 9.81 m/s2

How can we find the height?

vfy = 0 !

vy2 = voy

2 + 2ayΔy

O = (0.88 m/s)2 + 2(-9.81 m/s2) Δy

Δy = 0.039 m

Relative Velocity

If you are watching a person walk on the moving walkway and they are seem to be moving 5 mi/hr but you know they can only do 3 mi/hr, why is there a difference?

What we perceive is relative to us or the situation. vp + vw = vobs.

This is also apparent when you approach an intersection and you are going 35 mi/hr while they are going 45 mi/hr perpendicular to you.

You perceive the velocity to be the resultant?

What is it and at what angle ?

v = ((35mi/hr)2 + (45 mi/hr)2 )1/2

v = 57 mi/hr

θ = tan-1 (45/35) = 52o to the side of you.