Ch 3: 2-D motion & vectors Use arrows to show the direction and magnitude of vectors Scalar: just magnitude Vector: magnitude (length of vector) and direction tail head

Adding vectors graphically Must be the same units ( v&v or a&a ect) Resultant: sum of vectors, order does not matter.

Steps determine 0o north and list know vectors est. scale ( 1cm = 200m ect.) est. starting pt., place tail of 1st vector there with correct mag. & direction connect tail of 2nd to head of 1st ( correct mag. & direction) continue until all vectors added connect tail 1st to head last ( resultant) use scale to determine mag. and protractor to measure . cw rotation, add  to 1st vector direction. ccw rotation, subtract from 1st vector direction .

Board work A boy walks 5.0km north to a friends house and has lunch then walks 3.0km west to the hardware store to pick up a rake. What is his total distance and displacement? 8.0km, 5.8km at 31owest of north(329o) Two concurrent forces of 80.0Nsouth and 50.0Neast act on a body. What is the resultant force? 94.3N at 320 east of south(148o)

Continue Vectors add and act independently A boat traveling 5.0m/s west is moving through a river with a current of 1.5m/s south and is 100.0m wide. What is the boat’s resultant velocity? How long does it take to cross and how far down stream does the boat land? 5.2m/s at 17osouth of west(253o) t= 20.s d= 30m

Vector operations right x-axis and up y-axis, positive left x-axis and down y-axis negative coordinate system in two dimensions; break a vector into its x and y components ++ - + - - -+ Vr Vy Vx

Determine resultant vector 2 perpendicular vectors: cal. using Pythagorean theorem and tangent function Board work: A plane travels from Houston, Tx to Washington D.C. which is 1540km E and 1160km N of Houston. What is the planes total displacement? 1930km 37.0onorth of east ( 53.0o)

Resolving vectors into components( projections) Any vector can be completely described by a set of perpendicular components sin  =Vy/V cos  = Vx/V V Vy  Vx

Board work An arrow is shot from a bow at an angle of 25o above the horizontal with a velocity of 45m/s. determine the hor. (Vx) and vert (Vy) components of the arrows initial velocity. vh=41m/s and vv=19m/s vh>vv?

Vector addition A + B = ? 3A - 2B = ? Range of vector addition: V1=15 and V2= 25 Addition of several vectors B A A B C

Adding vectors not perpendicular Calculate the x and y component of each vector using sin and cos functions Add x and y components of each vector. Use trig. and pyth. functions to calculate the resultant vector. Board work: A plane flies 118km at 15.0oSofE then flies 118km 35.0oWofN. What is the total displacement? 81km at 55oNofE (35o)

Projectile motion Motion of objects moving in two dimensions under the influence of gravity Paths followed is a parabolic trajectories Will always have a horizontal velocity component of flight that is constant. ( neglect air resistance, no force in Vx direction) Projectile motion is free fall motion with an initial constant horizontal velocity and Vyi = 0 that is constantly changing.

2 motions vertical motion: Dy = vyit + 1/2gDt2 y = -1/2gt2 ( - from g) & vyf=-gt ( - from g) horizontal motion: x = vxt ( vx constant)

Board work People in movies often jump from buildings into pools. If a person jumps from the 10th floor(30.0m) to a pool that is 5.0m away from the building. What is the initial horizontal velocity the person must jump with? 2.0m/s

Projectiles at angles use components to analyze objects launched at angles vxi=vi(cos) Used to calculate Dx vyi=vi(sin) Used to determine time in flight. vi vyi  vxi

Cont. equations x = vi(cos)t : x=vxt : vx const. y=vi(sin)t - 1/2gt2 vyf=vi(sin) - gt vyf2=vi2(sin)2 - 2gy Derived: Vi = gDx/2sin  cos 

Drawing Vx Vyf = 0 g = -9.81m/s2 Constantly changing Vyi Vyf Vx Vx

Continue A football is kicked at an initial velocity of 20.0m/s at an angle of 35o. How high and how far does the ball travel? x = 38.4m y = 6.7m A batter hits a softball 100.0m at an angle of 40.0o. What was the initial velocity of the softball? 31.6m/s

Maximum hor. displacement

Frame of reference coordinate system for specifying the precise location of objects in space. velocity measurements differ in different frames of reference. internal external

F of R cont. A car is traveling 30km/hr north with another car traveling 20km/hr south behind the first car. What is the velocity of the second car relative to the first car? 50km/hr south A boy on a bus is walking toward the back at 3.0km/h while the bus travels south at 15km/h. The boys velocity to the road is 12km/h south

Board work A plane flies northeast at an airspeed of 563.0km/hr. A 48.0km/hr wind is blowing to southeast. What is the planes velocity relative to the ground? 565km/hr at 40.1oN of E( 49.9o)