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Exam 2
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Math 1321—001 Accelerated Calculus for Engineers IT
Spring 2013
• There are 100 total points in this exam.
• You have 50 minutes to complete the exam.
• Show all work, all steps, clearly and neatly, whenever possible.
• A half sheet, back and front, of notes is permitted.
• Please staple yonr note sheet to the exam before turning it in.
• The use of laptops, cell phones, and any other wireless devices are not allowed during this exam.
• Good luck!
Name:
1

1.) (10 pts) A sled is pulled along a level path through snow by a rope. A 20-lb force acting at an angle of 30 degrees above the horizontal moves the sled 190 ft. Find the work done by the force (reasonably simplify your answer and don’t forget units!).
2o.1Oes3O
2.) (10 pts) A gun fired with an angle of 45° at a height of 5 meters off the ground hits the ground 2500 meters away. What is the muzzle speed? (Gravity g
=
9.8m/s x=
-
qfrO)
Jxx
‘ a o fs o oo9:
-
L O
2

3.) (10 pts) Find the parametric equations and the symmetric equations for the line through
(1, 2, 0) and parallel to the vector (7, 1, 2). Reasonably simplify your answer.
-
L(1L
ri b2 v-I
a.
S vi C_
4.) (20 pts) Find the equation of the plane through the points (1, 2, 2), (4, 3, 1), and
(1, 1, 0) using a cross product (show all details in this computation). Provide your answer in the form ax + by + cz + d
=
0 and reasonably simplify the coefficients.
<[j k
I
3
-2
->
H)>
1 -
-I
\o-2\
0 -‘
i
-
C
°i
-0
+
-
-3#—(-3.*.1÷-Io
-
3

__
5.) (10 pts) Use the Squeeze Theorem to show that urn
(xy)—*(OO)
=
0.
—
2c
O
4

6.) Consider the space curve: r(t)
=
(/t, 3 sin t, 3 cost).
a.) (10 pts) Find the length of t.he curve from t
=
0 to t 30.
b.) (15 pts) Find acceleration a(t) and unit tangent and unit normal vectors T a.nd N.
c.) (15 pts) Choose one of the following:
If we decompose acceleration a(t)
= aTT + aNN, find aT. Considering what you found for a(t) and N, does your computation for aT make sense? Please explain.
OR
Find the curvature of r(t) and graph of r(t). Does your result for curvature make sense in light of the graph? Please explain.
‘
C)
S)
r::
-z
0
— q
—-
5
q
“k
‘
..
S
4
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