Motion Problems, Parametric, Vector-Valued Functions
AP Calculus BC · Flashcards
AP CALCULUS BC · FLASHCARDS
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QUESTION
What is the horizontal component of the velocity vector for
x
(
t
)
=
5
t
x(t)=5t
x
(
t
)
=
5
t
?
QUESTION
What is the parametric equation for
x
(
t
)
x(t)
x
(
t
)
of a projectile launched at angle
θ
\theta
θ
?
QUESTION
State the formula for the tangent vector of a parametric curve at
t
=
t
0
t = t_0
t
=
t
0
.
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ANSWER
T
(
t
0
)
=
v
(
t
0
)
∥
v
(
t
0
)
∥
\mathbf{T}(t_0) = \frac{\mathbf{v}(t_0)}{\|\mathbf{v}(t_0)\|}
T
(
t
0
)
=
∥
v
(
t
0
)
∥
v
(
t
0
)
. Unit vector formula using velocity magnitude.
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