Kinematics in Two or Three Dimensions
Vectors and Scalars
Vector
Scalar
has magnitude and direction
Eg: Displacement, velocity,force
magnitude only
Eg: Mass,Time, Temperature
Addition of vectors
one dimension
simple addition and subtraction
two dimension
Right angle
Not at right angle
Pythagorean Theorem
tail-to-tip method
Subtraction of Vectors and Multiplication of Vector by scalar
Negative of vector has same magnitude but different direction
Adding Vectors by Components
Vector is multiplied by a scalar c. cV has the same direction
Perpendicular components found using trigonometric function
One-dimensional components
-added arithmetically
Unit Vectors
Vector Kinematics
Projectile Motion
Horizontal
Vertical
-Acceleration is zero
-Velocity remains constant at any point
Acceleration(downwards)=
Relative velocity
Scalar product : a · b = |a| × |b| × cos(θ)
Vector product : |AxB| = A B sinθ.
Vbs =Vbw + Vws
Vbs is boat'svelocity
Vbw is boat's velocity(in water frame)
Vws is water's velocity(in shore frame)
Direction(angle)find using trigonometric function
Pythagorean theorem used to find the velocity
Low Jing Ning A20SC0126