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MATH
32A
Exam
2
November
29,
2007
LASTNAME
FIRST NAME
IDNO.
YourTA:
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credit,
you
must
write
your
answer
in
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DO NOT WRITE BELOW THIS LINE
1
(25 pts) 5
(25 pts)
2
(25 pts) 6
(25 pts)
3
(25 pts) 7
(25 pts)
4
(25 pts) 8
(25 pts)
TOTAL
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PROBLEM
1
(25
Points)
A miniature rocket leaves the origin at time t = 0 with
initial velocity(units are meters and seconds)
2
v0
Err:509
xy
onent h8,0i supplied by the rocket engines and a verti
2
cal component due to gravity of magnitude g m/sin the
downward direction. Use the approximate value g =10.
Answer:
(B)How far from the origin does the rocket land?
Answer:
A
' (t)
Solution:
(A)We have r
Err:509
r
(t)= th8,10i+ h40,40i
We have r(0)= h0,0i since the rocket begins at the origin.
Thus
r(t)=
1
t2h8,10i+ th40,40i
2
The rockeths acceleration vector a(t)has a horizontal comp
(A)Find the rockethsposition r(t)at time t.
(B)The rockethsycoordinateis 5t2
Page 3
+40t = 5t(t8), so
the rocketlands(crashes) attime t =8s. Thexcoordinate
is x =4t2
+40t, so the distance from the origin when the
rocket lands is
x(8)=4(82)+40(8)=576 m
x
PROBLEM
2
(25
Points)
Calculate the curvature of r(t)= ht,t1,t2i at t =1.
Answer:
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This test prep was uploaded on 04/21/2008 for the course MATH 31A taught by Professor Jonathanrogawski during the Fall '07 term at UCLA.
 Fall '07
 JonathanRogawski
 Math

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