Physics Chp 3 Trig Functions cos(θ) = x/h or =a/h sin(θ) =y/h or =o/h tan(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.

R 2 = x 2 +y 2 R = tan(θ) = y/x θ= If x = 3 and y = 2 find R

R 2 = R = tan(θ) = 2/3 θ= tan -1 (2/3) =

What about this? θ 11 8 R =? R is the resultant

Still R 2 = 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 v x = v ox +a x Δt Δx = 1/2(v o + v x )Δt Δx = v ox Δt + 1/2a x (Δt) 2 v x 2 = v ox 2 + 2a x Δx v y = v oy +a y Δt Δy = 1/2(v o + v y )Δt Δy = v oy Δt + 1/2a y (Δt) 2 v y 2 = v oy 2 + 2a y Δy

Ex How long does it take a ball kicked off a 45 m tall building to hit the ground? v oy = 0 y= -45m a y = -9.8 m/s 2 t = ?

Δy = v oy Δt + 1/2a y (Δt) 2 -45m = 0 + ½(-9.8m/s 2 )(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? v ox = 5.4 m/s ∆t = 3.0s a x = 0 ∆x =?

Δx = 1/2(v o + v x )Δt OR Δx = v ox Δt + 1/2a x (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 15 o above the horizontal, how high does the dog go? v o = 3.4 m/s θ = 15 o ∆y= ?

v ox = 3.4m/s cos15 o = 3.3 m/s a x = 0 v oy = 3.4m/s sin15 o = 0.88 m/s a y = m/s 2 How can we find the height?

v fy = 0 ! v y 2 = v oy 2 + 2a y Δy O = (0.88 m/s) 2 + 2(-9.81 m/s 2 ) Δy Δy = 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. v p + v w = v obs.

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) = 52 o to the side of you.