The parametric equations for the paths of two projectiles are given. At what rate is the distance between the two objects changing at the given value of t? X1 = 13 cos(2t), y1 = 6 sin(2t) X2 = 10 cos(t), y2 = 4 sin(t) First object Second object t = r/2 Step 1 Apply the distance formula to find the rate at which the distance is changing. Distance = f(t) = (X1 – x2)2 + (Y1 - Y2)² Differentiate f(t) with respect to t. f(t) = (13 cos 2t – 10 cos t)2 + (6 sin 2t – 4 sin t)2 V 1/2 X -1/2 . (금) f '(t) = (13 cos 2t – 10 cos t)2 + (6 sin 2t – 4 sin t)2| 0) * )(-26 sin 2t + 10 sin t) + (12 sin 2t – 8 sin t)(
The parametric equations for the paths of two projectiles are given. At what rate is the distance between the two objects changing at the given value of t? X1 = 13 cos(2t), y1 = 6 sin(2t) X2 = 10 cos(t), y2 = 4 sin(t) First object Second object t = r/2 Step 1 Apply the distance formula to find the rate at which the distance is changing. Distance = f(t) = (X1 – x2)2 + (Y1 - Y2)² Differentiate f(t) with respect to t. f(t) = (13 cos 2t – 10 cos t)2 + (6 sin 2t – 4 sin t)2 V 1/2 X -1/2 . (금) f '(t) = (13 cos 2t – 10 cos t)2 + (6 sin 2t – 4 sin t)2| 0) * )(-26 sin 2t + 10 sin t) + (12 sin 2t – 8 sin t)(
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter8: Polar Coordinates And Parametric Equations
Section8.FOM: Focus On Modeling: The Path Of A Projectile
Problem 7P: Shooting into the Wind Using the parametric equations you derived in Problem 6. draw graphs of the...
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The parametric equations for the paths of two projectiles are given. At what rate is the distance between the
two objects changing at the given value of t?
X1
= 13 cos(2t), Yı = 6 sin(2t)
First object
X2
10 cos(t), y2 = 4 sin(t)
Second object
t π/2
=
Step 1
Apply the distance formula to find the rate at which the distance is changing.
(x1- x2)2 + (Y1 – y2)?
Distance =
f(t) =
V
%D
Differentiate f(t) with respect to t.
f(t)
(13 cos 2t
10 cos t)2 + (6 sin 2t
4 sin t)2
1/2X
-1/2
f '(t) :
|(13 cos 2t
10 cos t)2 + (6 sin 2t – 4 sin t)2|
%D
-
)(-26 sin 2t + 10 sin t)| +
|(12 sin 2t – 8 sin t)(
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