Ch 3 2 -D motion vectors Use

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

Board work A boy walks 5. 0 km north to a friends house and has lunch then walks 3. 0 km west to the hardware store to pick up a rake. What is his total distance and displacement? 8. 0 km, 5. 8 km at 31 owest of north(329 o) Two concurrent forces of 80. 0 Nsouth and 50. 0 Neast act on a body. What is the resultant force? 94. 3 N at 320 east of south(148 o)

Continue Vectors add and act independently A boat traveling 5. 0 m/s west is moving through a river with a current of 1. 5 m/s south and is 100. 0 m 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. 2 m/s at 17 osouth of west(253 o) t= 20. s d= 30 m

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

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 1540 km E and 1160 km N of Houston. What is the planes total displacement? 1930 km 37. 0 onorth of east ( 53. 0 o)

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 25 o above the horizontal with a velocity of 45 m/s. determine the hor. (Vx) and vert (Vy) components of the arrows initial velocity. vh=41 m/s and vv=19 m/s vh>vv?

Vector addition A+B=? B A 3 A - 2 B = ? Range of vector addition: V 1=15 and V 2= 25 Addition of several vectors 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 118 km at 15. 0 o. Sof. E then flies 118 km 35. 0 o. Wof. N. What is the total displacement? 81 km at 55 o. Nof. E (35 o)

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: y = vyit + 1/2 g t 2 y = -1/2 gt 2 ( - 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 10 th floor(30. 0 m) to a pool that is 5. 0 m away from the building. What is the initial horizontal velocity the person must jump with? 2. 0 m/s

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

Cont. equations x = vi(cos ) t : x=vx t : vx const. y=vi(sin ) t - 1/2 g t 2 vyf=vi(sin ) - g t vyf 2=vi 2(sin )2 - 2 g y Derived: Vi = g x/2 sin cos

Drawing Vx Vyf = 0 g = -9. 81 m/s 2 Constantly changing Vyi Vx constant Vyf Vx

Continue A football is kicked at an initial velocity of 20. 0 m/s at an angle of 35 o. How high and how far does the ball travel? x = 38. 4 m y = 6. 7 m A batter hits a softball 100. 0 m at an angle of 40. 0 o. What was the initial velocity of the softball? 31. 6 m/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 30 km/hr north with another car traveling 20 km/hr south behind the first car. What is the velocity of the second car relative to the first car? 50 km/hr south A boy on a bus is walking toward the back at 3. 0 km/h while the bus travels south at 15 km/h. The boys velocity to the road is 12 km/h south

Board work A plane flies northeast at an airspeed of 563. 0 km/hr. A 48. 0 km/hr wind is blowing to southeast. What is the planes velocity relative to the ground? 565 km/hr at 40. 1 o. N of E( 49. 9 o)