vectorshonors.ppt
- 2. SCALAR A SCALAR quantity is any quantity in physics that has MAGNITUDE ONLY Number value with units Scalar Example Magnitude Speed 35 m/s Distance 25 meters Age 16 years
- 3. VECTOR A VECTOR quantity is any quantity in physics that has BOTH MAGNITUDE and DIRECTION Vector Example Magnitude and Direction Velocity 35 m/s, North Acceleration 10 m/s2, South Force 20 N, East An arrow above the symbol illustrates a vector quantity. It indicates MAGNITUDE and DIRECTION
- 4. VECTOR APPLICATION ADDITION: When two (2) vectors point in the SAME direction, simply add them together. EXAMPLE: A man walks 46.5 m east, then another 20 m east. Calculate his displacement relative to where he started. 66.5 m, E MAGNITUDE relates to the size of the arrow and DIRECTION relates to the way the arrow is drawn 46.5 m, E + 20 m, E
- 5. VECTOR APPLICATION SUBTRACTION: When two (2) vectors point in the OPPOSITE direction, simply subtract them. EXAMPLE: A man walks 46.5 m east, then another 20 m west. Calculate his displacement relative to where he started. 26.5 m, E 46.5 m, E - 20 m, W
- 6. Vectors are always added head to tail For example draw what you think it would look like if I added these two vectors together: A+B. Then draw what you think A-B would look like. A B A+B A-B
- 7. You try on the whiteboard A B C a.A+C b.B+C c.A-B d.C-B e.A+B
- 8. NON-COLLINEAR VECTORS When two (2) vectors are PERPENDICULAR to each other, you must use the PYTHAGOREAN THEOREM Example: A man travels 120 km east then 160 km north. Calculate his resultant displacement. 120 km, E 160 km, N the hypotenuse is called the RESULTANT HORIZONTAL COMPONENT VERTICAL COMPONENT S T A R T FINISH c2 a2 b2 c a2 b2 c resultant 120 2 160 2 c 200km
- 9. WHAT ABOUT DIRECTION? In the example, DISPLACEMENT asked for and since it is a VECTOR quantity, we need to report its direction. N S E W N of E E of N S of W W of S N of W W of N S of E E of S NOTE: When drawing a right triangle that conveys some type of motion, you MUST draw your components HEAD TO TOE. N of E
- 11. NEED A VALUE – ANGLE! Just putting N of E is not good enough (how far north of east ?). We need to find a numeric value for the direction. N of E 160 km, N 120 km, E To find the value of the angle we use a Trig function called TANGENT. Tan opposite side adjacent side 160 120 1.333 Tan1 (1.333) 53.1o 200 km So the COMPLETE final answer is : 200 km, 53.1 degrees North of East
- 12. What are your missing components? Suppose a person walked 65 m, 25 degrees East of North. What were his horizontal and vertical components? 65 m 25 H.C. = ? V.C = ? The goal: ALWAYS MAKE A RIGHT TRIANGLE! To solve for components, we often use the trig functions since and cosine. E m C H opp N m C V adj hyp opp hyp adj hypotenuse side opposite hypotenuse side adjacent , 47 . 27 25 sin 65 . . , 91 . 58 25 cos 65 . . sin cos sine cosine
- 13. Draw the vector diagram Combine ‘like’ vectors Determine the resultant AND the angle of direction A bear, searching for food wanders 35 meters east then 20 meters north. Frustrated, he wanders another 12 meters west then 6 meters south. Calculate the bear's displacement.
- 14. Example A bear, searching for food wanders 35 meters east then 20 meters north. Frustrated, he wanders another 12 meters west then 6 meters south. Calculate the bear's displacement. 35 m, E 20 m, N 12 m, W 6 m, S - = 23 m, E - = 14 m, N 23 m, E 14 m, N 3 . 31 ) 6087 . 0 ( 6087 . 23 14 93 . 26 23 14 1 2 2 Tan Tan m R The Final Answer: 26.93 m, 31.3 degrees NORTH or EAST R
- 15. Draw the vector diagram Combine ‘like’ vectors (if necessary) Determine the resultant AND the angle of direction A boat moves with a velocity of 15 m/s, N in a river which flows with a velocity of 8.0 m/s, west. Calculate the boat's resultant velocity with respect to due north.
- 16. Example A boat moves with a velocity of 15 m/s, N in a river which flows with a velocity of 8.0 m/s, west. Calculate the boat's resultant velocity with respect to due north. 15 m/s, N 8.0 m/s, W Rv 1 . 28 ) 5333 . 0 ( 5333 . 0 15 8 / 17 15 8 1 2 2 Tan Tan s m Rv The Final Answer : 17 m/s, @ 28.1 degrees West of North
- 17. A plane moves with a velocity of 63.5 m/s at 32 degrees South of East. Calculate the plane's horizontal and vertical velocity components. Draw the vector diagram Combine ‘like’ vectors (if necessary) Determine the resultant AND the angle of direction
- 18. Example A plane moves with a velocity of 63.5 m/s at 32 degrees South of East. Calculate the plane's horizontal and vertical velocity components. 63.5 m/s 32 H.C. =? V.C. = ? S s m C V opp E s m C H adj hyp opp hyp adj hypotenuse side opposite hypotenuse side adjacent , / 64 . 33 32 sin 5 . 63 . . , / 85 . 53 32 cos 5 . 63 . . sin cos sine cosine
- 19. A storm system moves 5000 km due east, then shifts course at 40 degrees North of East for 1500 km. Calculate the storm's resultant displacement. Draw the vector diagram Combine ‘like’ vectors (if necessary) Determine the resultant AND the angle of direction
- 20. Example A storm system moves 5000 km due east, then shifts course at 40 degrees North of East for 1500 km. Calculate the storm's resultant displacement. N km C V opp E km C H adj hyp opp hyp adj hypotenuse side opposite hypotenuse side adjacent , 2 . 964 40 sin 1500 . . , 1 . 1149 40 cos 1500 . . sin cos sine cosine 5000 km, E 40 1500 km H.C. V.C. 5000 km + 1149.1 km = 6149.1 km 6149.1 km 964.2 km R R 6149.12 964.22 6224.2km Tan 964.2 6149.1 0.157 Tan1 (0.157) 8.92o The Final Answer: 6224.2 km @ 8.92 degrees, North of East