Motion - 2 - Vectors and Displacement

University:
High School
Course:
High School Physics
Academic year:

2024
Views:

492

Pages:

20
Author:

1 1

Vectors & Displacement (Ch 8) Recall, A vector is a quantity with a magnitude, unit & direction Displacement is a vector 1.4 Vector Diagrams: Vector shown as an arrow Length of arrow = magnitude Direction of arrow = direction 20mm [30oS of E] 3cm [E] 6cm [45oW of S] 4cm [65oN of E] Note: can use a scale What Direction am I? N W E S 4   Every vector has vertical & horizontal components Ex. components 5m 3m 4m Can use Pythagoras & trig to solve for the vector, its components or its direction!!! 1.5 Vector Addition:   Vectors can be added together to give a resultant C B Ex. Distance Traveled = AB+BC Displacement = AC A Resultant   Use the tip-to-tail method Can then solve by either: 1. Ruler/Protractor 2. Trig (sine law, SOH CAH TOA, cosine law) 3. Pythagoras Order does not matter, BUT preserve orientation & length Ex 1  Solving for the resultant using trig: a2 + b2 = c2 12.02 + 5.02 = c2 H 12.0cm c = 13.0cm O 5.0cm A 13.0cm [67o N of W] 13.7m Ex 2 ! y r t u Yo A person walks 12.3m [W] then 13.7m [S]. Calculate the net/total displacement of this person. A 12.3m 18.4m [48.1o S of W] a2 + b2 = c2 H 12.32 + 13.72 = c2 c = 18.4m A plane flies 35.0km[W], then Ex 3 43.0km[N], then 62.0km[E]. What is the plane’s total displacement? 62.0km 27.0km 43.0km 43.0km 35.0km b/c 180o a2 + b2 = c2 43.02 + 27.02 = c2 c = 50.8km 50.8km [32.1o E of N] A person leaves school & walks home, Ex 4 for a total displacement of 1.00 x 102m at a direction of 40.0oS of E. How far east & how far south did this person walk? A O 100m H 76.6m East & 64.3m South A plane flies 200km[45.0oS of W], Ex 5 then changes direction & flies 300km[60.0oN of W]. (use 3 s.f.) What is the net displacement of the plane? Separate & solve each component Problem: Degrees!!! A plane flies 200km[45.0oS of W], Ex 5 then changes direction & flies 300km[60.0oN of W]. (use 3 s.f.) What is the net displacement of the plane? x y 200km A plane flies 200km[45oS of W], then changes direction & flies 300km[60oN of W]. What is the net displacement of the plane? 300km y x 315km [22.1o N of W] 118.39km North 291.42km West a2 + b2 = c2 118.39km 291.42km 118.392 + 291.422 = c2 c = 314.55km Ex 6 A hiker travels 5.00km [70.0oN of E] ! y r t u o then travels 1.00km [30.0oS of E]. Y What is the net displacement of the hiker? 5km y x Separate & solve each component A hiker travels 5.00km [70.0oN of E] then travels 1.00km [30.0oS of E]. What is the net displacement of the hiker? x 1km y 4.1985 km [N] 2.5761 km [E] a2 + b2 = c2 4.19852 + 2.57612 = c2 4.1985 2.5761 c = 4.9258 km 4.93 km [58.5o N of E] Summary of Steps: 1. Find the components of each vector in the problem (x and y). - Keep two more decimal places than required in final answer. 2. Add all x-components to find overall x-component (E +, W -) Add all y-components to find overall y-component (N +, S -) 3. Create final triangle and find - magnitude using Pythagorean Theorem - angle using tangent (or sine law) Express final displacement with magnitude and direction. Ex: Δd = 6.25 m [24.2° E of N] Note: Final answer matches same #of decimal places as given info. Quantum: Try: pg 189 #3ac, 4ac pg 192 #2bc pg 199 #4bc