Advanced Projectile Simulation Study

Aug 15, 2024

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Explore the intricate dynamics of projectile motion through a comprehensive simulation study. Gain insights into trajectories, velocities, and impacts of various projectiles in different scenarios.

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projectile dynamics study
simulation analysis
trajectory prediction
velocity impact analysis

ghenderson

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Advanced Projectile Simulation Study

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X-Y
X-Y
X-Y
X-Y
X-Y
Projectiles
Projectiles
Projectiles
Projectiles
Projectiles
Projectiles
Projectiles
Projectiles
Projectiles
Projectiles
Projectiles
Projectiles
Projectiles
Projectiles
Projectiles

x-y · 4

2D System of Inequalities. y. Consider the polyhedron Q = { ( x,y ) : -3x+y · 6 , x+y · 3, -y-2x · 5 , x-y · 4 }. -3x+y · 6. x+y · 3. x. Given x, for what values of y is ( x,y ) feasible? Need: y · 3x+6 , y · -x+3, y ¸ -2x-5 , and y ¸ x-4. x-y · 4. -y-2x · 5.

295 views • 10 slides

y 1 y 2 x 1 x 2

Y. v 1 v 2. motion path described by the particle on 2D. R 1. j = (0,1). R 2. y 1 y 2 x 1 x 2. i = (1,0). X. Using Cartesian Coordinates to Describe 2D Motion. P 1 P 2. R = x i + y j = ( x , 0) + (0, y ) = ( x , y ).

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f ( x,y ) = x 2 y + y 3 + 2 y

Definition of partial derivative (page 128-129). f ( x,y ) = x 2 y + y 3 + 2 y. ¶ f — = f x = ¶ x. ¶ f — = f y = ¶ y. 2 xy. x 2 + 3 y 2 + 2 y ln2. z = f ( x,y ) = cos( xy ) + x cos 2 y – 3. ¶ z — ( x,y ) = ¶ x. – y sin( xy ) + cos 2 y.

408 views • 11 slides

y = tan x

y = tan x. Recall from the unit circle: that tan  = tangent is undefined when x = 0. y=tan x is undefined at x = and x =. Domain/Range of the Tangent Function. The tangent function is undefined at + k  . Asymptotes are at every multiple of + k  .

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F (x, y) = <x, y>

F (x, y) = <y, -x>. F (x, y) = <x, y>. Div F = 0. Div F = 2 > 0. The divergence of a vector field at a point (x, y, z) corresponds to the net flow Of fluid out of a small box centered at (x, y, z). If Div F > 0, more fluid exits the

282 views • 16 slides

y = sec x

y = sec x. Recall from the unit circle that: sec = r/x. sec is undefined whenever x = 0. Between 0 and 2 , y = sec x is undefined at x =  /2 and x = 3  /2. Domain. Since sec x is undefined at  /2, 3  /2, etc., the asymptotes appear at  /2 + k . Range of Secant Function.

342 views • 16 slides

y = cot x

y = cot x . Recall that cot ï‘ = . cot ï‘ is undefined when y = 0. y = cot x is undefined at x = 0, x = ï° and x = 2 ï°. Domain/Range of Cotangent Function. Since the function is undefined at every multiple of ï° , there are asymptotes at these points.

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(define (f x) (if (< x 0) (lambda (y) (- y x)) (lambda (y) (- x y))))

GE. f:. P1. para:x body:(if … ). (define (f x) (if (< x 0) (lambda (y) (- y x)) (lambda (y) (- x y)))). GE. f:. foo:. P1. P2. para:x body:(if … ). para:bar,x,y body :(let … ). (define (f x) (if (< x 0) (lambda (y) (- y x)) (lambda (y) (- x y)))).

251 views • 13 slides

y=f(x)

The function. has no inverse. f(x1)=f(x2)=f(x3)=y, so. y. y=f(x). y. x. x1. x2. x3. has no inverse. But if we treat g as a function. then it does have an inverse. y. y=g(x). y. x. y. y=f(x). x. Graphs of a function and its inverse are reflections in the line y=x. y.

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K Y X

RUSH. ___________. K Y X. ___________. K. KYX: A Brief History.

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y – y 1 = m(x – x 1 )

Equation of a Straight Line. y – y 1 = m(x – x 1 ). x coordinate. y coordinate. slope. This allows use to find the equation of a straight line if we know its slope and one coordinate it passes through. Find the equation of the line (a) passing through (-2 , 3) with slope = 3

304 views • 8 slides

X,Y scatterplot

X,Y scatterplot. These are plots of X,Y coordinates showing each individual's or sample's score on two variables. When plotting data this way we are usually interested in knowing whether the two variables show a "relationship", i.e. do they change in value together in a consistent way?.

1.14k views • 81 slides

1. x = y = 2 . x = 13; y =

1 st Nine Weeks Exam Review Answers. 1. x = y = 2 . x = 13; y = 3. x = ; y = 14 4. x = ; y = 5. x = 6; y = 6. 7. 8. 9. 10. c os (A) = sin (B) 11. sin (A) = cos (B).

218 views • 11 slides

y = csc X

y = csc X. Recall from the unit circle that csc  = r/y. csc  is undefined whenever y = 0. y = csc x is undefined at x = 0 , x =  and x= 2 . Domain of Cosecant Function.

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Find f x and f y. f ( x, y ) = x 5 + y 5 + x 5y

1. 2. 3. 4. Find f x and f y. f ( x, y ) = x 5 + y 5 + x 5y. f x = 5x 4 + 5x 4y, f y = 5y 4 + x 5 f x = 2x + 2xy, f y = 2y + x 2 f x = 3x 2 + 3x 2y, f y = 3y 2 + x 3 f x = 4x 3 + 4x 3y, f y = 4y 3 + x 4. 1. 2. 3. 4.

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y = f(x)

y. y = f(x). f i (x). x o. x. x. ∆x i.

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Rotations Rotate 90⁰ Clockwise: ( x,y )→(y,-x) Rotate 90⁰ Counterclockwise:( x,y )→(- y,x )

Alternate interior angles : [ ∠2 and ∠7] , [ ∠6 and ∠3] Pairs are CONGRUENT Alternate Exterior angles : [ ∠1 and ∠8] , [ ∠5 and ∠4] Pairs are CONGRUENT Corresponding Angles : [ ∠1 and ∠3] , [ ∠2 and ∠4] , [ ∠5 and ∠7 ] , [ ∠6 and ∠8] Pairs are CONGRUENT

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y = x 2

y = 2 x 2. (2,8). y = x 2. (2,4). Consider dilating the graph of y = x 2. y. 15. by a factor of 2 from the x -axis. 10. The point ( x , y ) maps onto the point ( x , 2 y ). 5. . (2, 8). e.g. (2, 4). x. -3. -2. -1. 0. 1. 2. 3. y = 3 x 2. (2,12). y = x 2. (2,4).

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e.g.: Q(x, y): x + y = 0, then (  x)(  y)Q(x, y):

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y 1 y 2 x 1 x 2

82 views • 5 slides

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Advanced Projectile Simulation Study

Advanced Projectile Simulation Study

Presentation Transcript

x-y · 4

y 1 y 2 x 1 x 2

f ( x,y ) = x 2 y + y 3 + 2 y

y = tan x

F (x, y) = &lt;x, y&gt;

y = sec x

y = cot x

(define (f x) (if (&lt; x 0) (lambda (y) (- y x)) (lambda (y) (- x y))))

y=f(x)

K Y X

y – y 1 = m(x – x 1 )

X,Y scatterplot

1. x = y = 2 . x = 13; y =

y = csc X

Find f x and f y. f ( x, y ) = x 5 + y 5 + x 5y

y = f(x)

Rotations Rotate 90⁰ Clockwise: ( x,y )→(y,-x) Rotate 90⁰ Counterclockwise:( x,y )→(- y,x )

y = x 2

e.g.: Q(x, y): x + y = 0, then (  x)(  y)Q(x, y):

y 1 y 2 x 1 x 2

F (x, y) = <x, y>

(define (f x) (if (< x 0) (lambda (y) (- y x)) (lambda (y) (- x y))))