Vectors Displacement A vector is a quantity with

Vectors & Displacement

¡ A vector is a quantity with a magnitude, unit & direction ¡ Displacement is a vector ¡ One or two dimensional

Vector shown as an arrow ¡ Length of arrow = magnitude ¡ Direction of arrow = direction ¡ 20 mm [E 30 o. S] 3 cm [E] 6 cm [S 45 o. W] 4 cm [E 65 o. N] Note: can use a scale

Every vector has vertical & horizontal components ¡ Ex. components 5 m 3 m ¡ 4 m Can use Pythagoras & trig to solve for the vector, its components or its direction!!!

Vectors can be added together to give a resultant C B ¡ Ex. ¡ Distance Traveled = ABC Displacement = AC A Resultant

¡ ¡ Use the tip-to-tail method Can then solve by either: 1. 2. Ruler/Protractor Trig & Pythagoras*** Order does not matter, BUT preserve orientation & length

¡ Measuring resultant using a ruler & a protractor: 20 m [N 65 o. E] [E 25 o. N]

¡ Measure resultant using Pythagoras & trig O H 12 cm 5 cm A a 2 + b 2 = c 2 122 + 52 = c 2 c = 13 cm [W 67 o N]

A person walks 12. 3 m [W] then 13. 7 m [S]. Calculate the net/total displacement of this person. A 12. 3 m O 13. 7 m H 18. 41 m [W 48 o S] a 2 + b 2 = c 2 12. 32 + 13. 72 = c 2 c = 18. 41 m

A plane flies 35 km[W], then 43 km[N], then 62 km[E]. What is the plane’s total displacement? 62 km 27 km 43 km 35 km b/c 180 o a 2 + b 2 = c 2 432 + 272 = c 2 c = 50. 77 km [N 32 o E]

A person leaves school & walks home, for a total displacement of 100 m at a direction of [E 40 o. S]. How far east & how far south did this person walk? A O 100 m H 76. 60 m East & 64. 28 m South

A plane flies 200 km[W 45 o. S], then changes direction & flies 300 km[W 60 o. N]. What is the net displacement of the plane? x y 200 km Separate & solve each component Problem: Degrees!!!

A plane flies 200 km[W 45 o. S], then changes direction & flies 300 km[W 60 o. N]. What is the net displacement of the plane? 300 km y x

341. 55 km [W 22 o N] 118. 39 km North 118. 39 km 291. 42 km West a 2 + b 2 = c 2 118. 392 + 291. 422 = c 2 c = 341. 55 km

A hiker travels 5 km [E 70 o. N] then travels 1 km [E 30 o. S]. What is the net displacement of the hiker? 5 km y x Separate & solve each component

A hiker travels 5 km [E 70 o. N] then travels 1 km [E 30 o. S]. What is the net displacement of the hiker? x 1 km y

4. 93 km [E 58 o N] 4. 2 km North 2. 58 km East a 2 + b 2 = c 2 2 + 2. 582 = c 2 4. 2 km c = 4. 93 km 2. 58 km