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# Scalars And Vectors Joshuas Fang Xu Shao Yun

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### Scalars And Vectors Joshuas Fang Xu Shao Yun

1. 1. TAN SHAO YUN 3S2 LIU FANG XU 3S3 JOSHUA NG 3S4 JOSHUA YEO 3S4 SCALARS AND VECTORS
2. 2. SCALARS VECTORS REPRESENTING A VECTOR DIRECTION OF VECTOR THE RESULTANT COMMON TERMS USED
3. 3. SCALAR A scalar has a numerical quantity only. Examples  Distance  55km  Temperature  30° c  Time  32 seconds  Anything else  9000 points
4. 4. VECTORS Vectors, unlike scalars, have both a magnitude and a direction. Examples  1D displacement  -22m  +63km  2D displacement  22m northeast  63km north
5. 5. REPRESENTING A VECTOR Represented by scaled vector diagrams Arrow pointing in specific direction Scale listed Magnitude of vector labelled (arrow drawn according to scale) Direction of vector labelled (degrees) Eg.
6. 6. DIRECTION OF VECTOR The direction of vector is the anti-clockwise angle of rotation which the vector makes with due East
7. 7. THE RESULTANT The vector sum of all the individual vectors. The result of combining the individual vectors together Determined by adding the individual forces together using vector addition methods. The direction of a resultant vector can often be determined by use of trigonometric functions. Can also be obtained by the head to tail method(best method).
8. 8. GRAPHICALLY MATHEMATICALLY WAYS OF DETERMINING RESULTANTS
9. 9. DETERMINING RESULTANT (GRAPHICALLY)  Resultant=sum of 2 or more vectors.  By drawing a graph we can tell the resultant of 2 or more vectors.  For example, given   By moving B to the end of A, and C to the end of B, we can tell the total distance and direction.  We can get the resultant by drawing a line from the start to  the end of C.
10. 10. EXAMPLE OF THE HEAD TO TAIL METHOD Two different vectors add up to form… The Resultant!
11. 11. DETERMINING RESULTANT (MATHEMATICALLY) Car A travels 6m eastwards and 8m northwards. a)What is its displacement towards the northeast? b)What is the direction of vector from car A’s starting point? Displacement = sqrt(6²+8²) = sqrt(100) = 10 Direction = sin ¹(8÷6)⁻ = 53.1°
12. 12. SAMPLE QUESTION A car travels 300m North from point A to point B, turns 90° clockwise and travels a further 400m to point C. a)What is the total distance he has travelled? b)What is his total displacement? AB = 300m BC = 400m AB+BC=AC 300m+400m=700m The total distance is 700m
13. 13. SAMPLE: PART B) To illustrate it better, we need a diagram. A B 300m 400m C ?m
14. 14. SAMPLE: PART B) B 400m C ?m A 300m Through Pythagoras's theorem: AB²+BC²=AC² AC=√AB²+BC² AC=√2500m = 500m Angle A= tan-1 (400/300) = 53.1° Therefore: The car’s displacement is 500m to 53.1° NE. 500m