Scalar & Vector Quantities

Science Starter Complete the maze using straight lines! Then, measure the lines using a ruler Leave column three blank for now

Scalars vs. Vectors Scalars Vectors Quantities that have size but no direction Examples: volume, mass, distance, temp Vectors Quantities that have both size and direction Examples Force Velocity Magnetic fields Size Terminal point Initial point

SCALAR QUANTITIES •Described by a single number and unit of measurement. •Gives the magnitude (size) Examples Mass = 20 g Time = 20.0 s Temperature = 20oC Speed = 20 m/s DISTANCE

VECTOR QUANTITIES •Arrows are used •Described by a single number and a unit of measurement (scalar) •Indicated direction. (head of arrow) Examples 30 m/s, East 30 m/s, N of E DISPLACEMENT

Vectors Representation Magnitude of a vector Equal vectors B Representation Letters with arrows over them Component form: <0,2> Magnitude of a vector Length of the vector, always positive Designated |K| Equal vectors Same magnitude and Same direction C

DETERMINING DIRECTION A B N of E N of W S of E C D S of W

ADDITION OF COLLINEAR VECTORS Resultant vector represent the total of two or more vectors

VECTORS ACTING IN THE SAME DIRECTION Connect them head-to-tail and add Always indicate the direction of the the resultant 10 km 10 km R = 20 km, 0o E

VECTORS ACTING IN OPPOSITE DIRECTIONS Connect them tail to tail Subtract 20 km 10 km R = 10 km, 0o, W

VECTORS ACTING AT A RIGHT ANGLE TO EACH OTHER •Connect head-to-tail •Draw resultant from the tail of the lst vector to the head of the second vector. •Determine resultant using pythagorean theorem •Determine angular direction by using the tan function

Pythagorean Theorem C2 = a2 + b2 C = hypotenuse A & B are sides

R = 22 km = 20 km R2 = (10 km)2 + (20 km)2 20 km 10 km 10 km or 20 km

Trig of the Right Triangle hypotenuse Opposite side Ө Adjacent side

DETERMINING DIRECTION OF RESULTANT DRAW TRIANGLE USING SUMS OF X- AND Y-COMPONENTS R 46 Paces N of W 88 Paces

VALUE OF RESULTANT Use Pythagorean Theorem R2 = (88 paces)2 + (46 paces)2 R = 99 paces

Independent Practice Now complete column three of the maze When finished, work on worksheet!