Vectors In 2-dimensions And Projectile Motion Flashcards
Vector diagram
Point of origin=tail, terminal point= tip, length of line segment depends on the vectors magnitude. Draw connecting vectors from tip to tail
Can only add vectors representing the same types of quantities
Reference Coordinate
Establish positive and negative, where you are going OF where you’re coming from
Collinear
Along the same straight line, either in the same or in opposite directions
Resultant vector
A vector drawn from the tail of the first vector to the top of the last vector
Change in d= dfinal-dinitial
Components
Perpendicular parts into which a vector can be separated (diagonal motion)
Polar Coordinates method
Positive x axis is at 0 degrees, angles measured by moving counterclockwise about the origin
Navigator method
Uses compass bearings north, south, east, and west to identify vector directions. To draw this vector, start with the second compass bearing you are given in brackets then move __degrees in the direction of the first compass bearing you are given
Non-collinear
Vectors that are not along the same straight line, determine magnitude/direction of the sum of 2 or more non-collinear vectors graphically.
To find displacement in 2 dimensions add the 2 position vectors
Steps for adding non-collinear vectors graphically
- Create appropriate time
- Choose a set of reference coordinates
- Draw vector 1 to scale
- Draw vector 2 to scale (tip to tail)
- Draw resultant vector
- Measure magnitude and direction of the resultant from its tail
- Use scale to convert magnitude of resultant to original units
- state resultant vector(magnitude and direction)
Determining Components
c^2=a^2+b^2
SOHCAHTOA
Adding vectors using components
Write the magnitude of any 2 dimensional vector as the sum of its x and y components (perpendicular)
A change in one component does not affect the other component
Use Pythagorean theorem, use inverse tan function to find the angle
Steps for adding non-collinear vectors algebraically
- Determine x and y components of each vector
- Add all components in the x direction, add all components in the y direction (sums of x and y components are the 2 components of resultant vector)
- Find magnitude of resultant vector(pythagorean theorem), and angle using trigonometric ratios
Relative motion
Motion measured with respect to an observer
Ground velocity
Velocity relative to an observer on the ground
Air velocity
An objects velocity relative to still air
Wind velocity
Velocity of the wind relative to the ground
relative motion in water
Water craft and swimmers experience currents, can move with current (ground velocity increases), against current (ground velocity decreases), or at an angle (ground velocity can increase or decrease)
*object moves at an angle to current both objects speed and direction change
Trajectory
The parabolic motion of a projectile, depends on initial velocity and the acceleration due to gravity. Consider horizontal (x direction) and vertical ( y direction)
Are independent of each other, gravity has no effect on objects horizontal motion
Horizontal motion
Of a projectile is uniform motion, velocity component is constant
Vertical motion
Of a projectile is uniformly accelerated motion, acceleration is constant due to gravity (9.81m/s^2 down)
Range
Distance a projectile travels horizontally over level ground
X direction of projectile
No acceleration, undergoes uniform motion. Initial x velocity usually Vicos0
Range is initial x velocity times time
Time is the same in both x And y directions
Y direction of a Projectile
Acceleration (-9.81m/s^2), initial velocity is usually Vi sin0. Displacement is Viyt+1/2at^2
Time is same in both x and y directions
projectiles velocity is greatest at the instant of launch and just before impact, max height velocity =0
