Adanced Kinematics I. Vector addition/subtraction II. Components III. Relatie Velocity IV. Projectile Motion V. Use of Calculus (nonuniform acceleration) VI. Parametric Equations
The student will be able to: 1 Calculate the components of a ector gien its magnitude and direction. Calculate the magnitude and direction of a ector gien its components. 3 Use ector components as a means of analyzing/soling -D motion problems. HW: 1 3 4 5 6 4 Add or subtract ectors analytically (using trigonometric calculations). 7 9 5 Use ector addition or subtraction as a means of soling relatie motion problems. 6 State the horizontal and ertical relations for projectile motion and use the same to sole projectile problems. 7 Use deriaties to determine speed, elocity, or acceleration and sole for extrema and/or zeros. 8 Use integrals to determine distance, displacement, change in speed or elocity and sole for functions thereof gien initial conditions. 9 Sole problems inoling parametric equations that describe motion components 10 15 16 4 5 7 8 31 3 34
Frame of Reference Any quantity of motion must be measured relatie to a certain frame of reference. A frame of reference is something with which a moing object is compared. The alues of position, elocity, acceleration, etc. depend upon the chosen frame of reference. (The alues could be anything, depending on which frame of reference is used)
Relatie Velocity Equation The alue of object A s elocity in reference frame C differs from that in reference frame B by the elocity of B relatie to C: AC AB + BC
Relatie Kinematics Equations The same type of relationship exists for position and acceleration: r a AC AC AC r a AB AB AB + r + + a BC BC BC
Consider a person walking on a moing sidewalk (often found in an airport). The net elocity is the ector sum of the person s walking elocity walking plus the elocity of the sidewalk. PE person relatie to earth PS + person relatie to sidewalk SE sidewalk relatie to earth
Adanced Kinematics I. Vector addition/subtraction II. Components III. Relatie Velocity IV. Projectile Motion V. Use of Calculus (nonuniform acceleration) VI. Parametric Equations
The student will be able to: 1 Calculate the components of a ector gien its magnitude and direction. Calculate the magnitude and direction of a ector gien its components. 3 Use ector components as a means of analyzing/soling -D motion problems. HW: 1 3 4 5 6 4 Add or subtract ectors analytically (using trigonometric calculations). 7 9 5 Use ector addition or subtraction as a means of soling relatie motion problems. 6 State the horizontal and ertical relations for projectile motion and use the same to sole projectile problems. 7 Use deriaties to determine speed, elocity, or acceleration and sole for extrema and/or zeros. 8 Use integrals to determine distance, displacement, change in speed or elocity and sole for functions thereof gien initial conditions. 9 Sole problems inoling parametric equations that describe motion components 10 15 16 4 5 7 8 31 3 34
What is a projectile? A projectile is an object launched by some initial force, which then proceeds under the sole influence of graity. The equations used to model this motion apply to the subsequent motion of the object after launch and before impact.
Projectile x and y Horizontally a projectile moes forward at a constant rate. The x-component of a projectile s elocity is constant.
Diameter of ball: 6.7 cm Strobe: 1800 flashes/minute 1 3 4 5 6 7 8 1 3 4 5 6 7 8 9 10 The ball has fallen 8 diameters after 10 flashes of the strobe light. What is its ertical acceleration?
Projectile x and y Horizontally a projectile moes forward at a constant rate. The x-component of a projectile s elocity is constant. Vertically a projectile moes with constant acceleration caused by graity. The y-component of a projectile s acceleration is g. The forward motion of a projectile does not alter the effect of graity nor does the force of graity alter the forward motion of a projectile.
d + at 0 t + 1 at 0 a x? a y? d a t 0 x t + a t x 0x x + x x 1 d a t 0 y t + a t y 0 y y + y y 1
d + at 0 t + 1 at 0 ax d 0 a t 0 x t + a t x 0x x + x x 1 a y d g a t 0 y t + a t y 0 y y + y y 1
t a y y y + 0 1 0 t a t y y y + Δ x x 0 t x x 0 Δ at + 0 1 0 t a t d + 0 x a g a y
Components of Projectile Motion Horizontal ax x 0x Δx 0 0x t a y Δy Vertical g a t 0 y t + a t 0 y y + y y 1
a d 0
a x 0 0y d Δy y 0x Δx
Components of Projectile Motion Horizontal ax x 0x Δx 0 0x t a y Δy Vertical g a t 0 y t + a t 0 y y + y y 1
Although seldom done it is also alid to not use components and instead use ector diagrams such as those shown here to analyze projectile motion. 0 t at ½ 0 at 0 + at 0 d d t + 1 at 0