Due Next Class: U2.HW2.Vectors All. Do Now: 1. Walk in silently. 2. Grab a calculator and any papers for today.

Transcription

1 Do Now: 1. Walk in silently. Due Next Class: U2.HW2.Vectors All 2. Grab a calculator and any papers for today. 1. If the cliff is 35m high, 2. how far from the bottom 3. of the cliff will the ball hit 4. the water?

2 REMINDERS! Retakes are required if you failed 3 or more sections. Denoted by an R on your mastery sheet You must first attend Exam tutoring (and sign in), before you will be allowed to retake. (Bring your mastery sheet) RETAKE DATES: WED, THURS, AND FRIDAY (9 th, 10 th & 11 th ) afterschool only. Sign ups on my door. First come first serve.

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5 Why it matters in LIFE: Part of being a functional human being is being able to understand what s happening in the world around you! By the end of today, IWBAT -Find components of vectors by using SOH CAH TOA - Find the hypotenuse (resultant) vector by using the Pythagorean Theorem - Find the direction of a vector using inverse tangent Why it matters in THIS CLASS: Our Goal = 80% Mastering today s lesson (focused participation, asking questions, etc) is the first brick that will help us reach our goal for this unit, and eventually for the year

6 TEKS: 4(B) describe and analyze motion in one dimension using equations with the concepts of distance, displacement, speed, average velocity, instantaneous velocity, and acceleration; By the end of today, IWBAT -Find components of vectors by using SOH CAH TOA - Find the hypotenuse (resultant) vector by using the Pythagorean Theorem - Find the direction of a vector using inverse tangent Topic: Vectors and Angles

7 LAST CLASS HORIZONTAL PROJECTILES

8 BUT WHAT IF WE STARTED AT AN ANGLE?

9 BUT WHAT IF WE STARTED AT AN ANGLE?

10 VECTORS Vectors have both direction & magnitude

11 VECTORS 45 Vectors have both direction & magnitude

12 VECTORS Vectors can be broken into x and y components

13 VECTORS EXAMPLE 5 m/s 10 degrees from vertical 34 m/s 40 degrees from horizontal 15 m/s 0 degrees from vertical

14 VECTORS Sketch these 4 vectors in your notes then draw the x and y components. 51 m/s 34 degrees from horizontal 4 m/s 14 degrees from vertical 2 m/s 0 degrees from horizontal

15 *REMINDER!* VECTORS θ x and y components can be calculated using SOH CAH TOA SOH sin θ = opposite hypotenuse CAH cos θ = adjacent hypotenuse TOA tan θ = opposite adjacent

16 VECTORS SOH sin θ = opposite θ hypotenuse CAH cos θ = adjacent KP: Vectors can be broken hypotenuse into x and y components using SOH CAH TOA TOA tan θ = opposite adjacent

17 *REMINDER!* VECTORS θ x and y components can be calculated using SOH CAH TOA SOH sin θ = opposite hypotenuse CAH cos θ = adjacent hypotenuse TOA tan θ = opposite adjacent

18 VECTORS Label the sides as opposite, adjacent, or hypotenuse in reference to the green angle.

19 VECTORS EXAMPLE FIND THE X AND Y COMPONENTS OF INITIAL VELOCITY cos(51) = Vix. 62 Vix = 62*cos(51) Vix = 62* Vix = m/s 51 Vix Viy sin(51) = Viy. 62 Viy = 62*sin(51) Viy = 62* Viy = m/s

20 VECTORS YOU TRY FIND THE X AND Y COMPONENTS OF INITIAL VELOCITY cos(63) = Vix. 87 Vix = 87*cos(63) Vix = 87* Vix = m/s 63 Viy sin(63) = Viy. 87 Viy = 87*sin(63) Viy = 87* Viy = m/s Vix

21 VECTORS YOU TRY FIND THE X AND Y COMPONENTS OF INITIAL VELOCITY cos(-17) = Vix. 38 Vix = 38*cos(-17) Vix = 38* Vix = m/s Vix -17 Viy sin(-17) = Viy. 38 Viy = 38*sin(-17) Viy = 38* Viy = m/s

22 COMBINING VECTORS r θ y x Vector components (x and y) can be combined to find the resultant vector s magnitude and direction.

23 *REMINDER!* COMBINING VECTORS r y x Resultant vector s magnitude is found using the Pythagorean Theorem. Pythagorean Theorem x 2 + y 2 = r 2 or r = x 2 + y 2

24 COMBINING VECTORS θ y Resultant vector s direction is found using inverse tan (tan -1 ). x

25 COMBINING VECTORS EXAMPLE FIND THE MAGNITUDE AND DIRECTION OF THE RESULTANT INITIAL VELOCITY r = x 2 + y 2 r = r = r = r = 5.41 m/s r θ Viy = 3 m/s tanθ = y x tanθ = tanθ = Vix = 4.5 m/s tan 1 (tanθ) = tan 1 ( ) θ = 33.69

26 COMBINING VECTORS YOU TRY FIND THE MAGNITUDE AND DIRECTION OF THE RESULTANT INITIAL VELOCITY r = x 2 + y 2 r = r = r θ Vix = 34 m/s Viy = 17 m/s tanθ = y x tanθ = tanθ = 0.5 r = 1445 r = m/s tan 1 (tanθ) = tan 1 (0.5) θ = 26.57

27 COMBINING VECTORS YOU TRY FIND THE MAGNITUDE AND DIRECTION OF THE RESULTANT INITIAL VELOCITY r = x 2 + y 2 r = ( 0.61) 2 r = r = r = 0.67 m/s Vix = 0.27 m/s r θ tanθ = y x Viy = m/s tanθ = tanθ = tan 1 (tanθ) = tan 1 ( ) θ = 66.12

28 INDEPENDENT PRACTICE! Procedure for IP time: 1) Silent work time 2) Try and solve without notes first! Hierarchy of who to ask 1) Your brain 2) Your notes 3) Your partner (quiet whisper) 4) Ms. Kelly

29 VECTORS EXIT TICKET 1. Find the x and y components of initial velocity. 2. Find the magnitude (r) and direction (θ 1 ) of the resultant vector. Bonus: find θ 2 82 Viy r θ 1 θ 2 Viy = 7 m/s Vix Vix = 4 m/s

30 VECTORS SWAP & MARK 1. Find the x and y components Vix = 1.70 Viy = Find the magnitude (r) and direction (θ 1 and θ 2 ) of the resultant vector. r = 8.06 θ 1 = Bonus! θ 2 = 29.74

31 TRIG FOR RIGHT TRIANGLES! NOTES

32 TRIG! NOTES Label the sides as opposite, adjacent, or hypotenuse in reference to the green angle.

33 TRIG! NOTES SOH sin θ = opposite hypotenuse CAH cos θ = adjacent hypotenuse TOA tan θ = opposite adjacent

34 TRIG FOR RIGHT TRIANGLES! EXAMPLE

35 TRIG FOR RIGHT TRIANGLES! EXAMPLE

36 TRIG FOR RIGHT TRIANGLES! YOU TRY

37 TRIG FOR RIGHT TRIANGLES! YOU TRY 1. Find z using the 30 angle. 2. Find z using the 60 angle. 3. Find z using Pyth. The.

38 DO NOW 1. CHECK YOUR NAME ON THE REQ. TEST CORRECTIONS LIST ON THE BOARD 1. Find z using the 30 angle. 2. Find z using the 60 angle. 3. Find z using Pyth. The.

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40 PYTHAGOREAN THEOREM FOR RIGHT TRIANGLES! NOTES a 2 + b 2 = c 2

41 PYTHAGOREAN THEOREM FOR RIGHT TRIANGLES! EXAMPLE

42 PYTHAGOREAN THEOREM FOR RIGHT TRIANGLES! EXAMPLE

43 PYTHAGOREAN THEOREM FOR RIGHT TRIANGLES! YOU TRY