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MATH 231
Group Work
Quiz Related
1. Compute
T
(
t
),
N
(
t
),
B
(
t
) and
κ
(
t
) for the following curves:
(a)
r
(
t
) =
t
3
j

4
t
k
(b)
r
(
t
) =
1
2
sin
t
i
+
1
2
cos
t
j
+
1
2
t
k
2. A gun is ﬁred with angle of elevation 30
◦
. What is the muzzle speed if the maximum height of a shell
is 500 m?
3. At what point does the curve have maximum curvature?
(a)
y
=
x
4
(b)
y
= ln
x
4. The position function of a particle is given by
r
(
t
) =
±
5
t
2
,t,t
2

16
²
. When is the speed minimal?
5. Find the equations of the normal and osculating planes for the functions in
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Unformatted text preview: (1) at time t = 0. 6. At what point on the curve x = t 3 , y = 3 t , x = t 4 is the normal plane parallel to the plane 6 x +6 y8 z = 1? 7. A man throws a football to his son who is 30 ft away. The ball leaves his hand at an angle of 30 ◦ and a speed of 5 ft/s. How high will his son need to reach to catch the ball? 1...
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This homework help was uploaded on 04/17/2008 for the course MATH 231 taught by Professor Bociu during the Spring '08 term at UVA.
 Spring '08
 BOCIU
 Math, Calculus

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