Homework Assignment # 3
Math 114 Section 2, Spring 2014
INSTRUCTOR : Prof. Wolfgang Ziller
due Tuesday February 11
This homework consists of two parts. The first part are online problems from the book
to be completed in My Math Lab. When you log into MyMathLab with your access code,
you will see that Assignment 2 is now available These problems are graded automatically
by the computer system and you can keep track of what your score is as the semester
goes along.
The second part are a few Past Final Exams Problems, which for your convenience are
listed on the following pages (see also
http://www.math.upenn.edu/ugrad/calc/m114/oldexams.html
for a complete list of Past Final Exam problems). The Past Final Exams Problems need
to be handed in to me at the end of class Tuesday February 11. No late homework
will be accepted!
The homework needs to be turned in in your own hand writing, no copies or scanned
versions are allowed! Please write legibly since one problem (picked at random) will
be graded each week. You can work on problems together (I encourage you to form
study groups), but the write up you should do on your own. My reasoning for this
requirement (besides discouraging cheating) is that if you write it up yourselves, after
possibly discussing the problems with others, you will have a much better understanding
of the material. (Maybe you only thought you understood it). If we discover exact copies
of the homework solutions, neither one will get credit.
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4
(3) An Iraqi reporter throws his shoe at President Bush during the President’s last
press conference in Bagdad.
The reporter is a horizontal distance of 12 feet from the President, and launches
his shoe from a height of 3 feet. At lift-off, the shoe has a speed of 24 feet per
second, and its trajectory makes an angle of 45◦ with the horizontal. The only
force acting on the shoe during its flight is gravity, which produces a downward
acceleration of 32 feet/sec2 .
How high will the shoe be above the ground when it is over the position where
the President is standing? (You should treat the shoe as a point object; ignore the
fact that it actually was a size 12 tasselled loafer.)
(A) 6 feet
(B) 5 feet
(C) 3 feet
(D) 8 feet
(E) 7 feet
(F) none of the above.
Answer to 3:
Math 114 Hand-In HW # 3
Spring 2013-Rimmer
Fall 2010
Name___________________________________
Recitation Number _________________________
Math 114 Hand-In HW # 3
Spring 2013-Rimmer
Fall 2010
Name___________________________________
Recitation Number _________________________
Math 114 Hand-In HW # 3
Spring 2013-Rimmer
Fall 2009
Name___________________________________
Recitation Number _________________________
Math 114 Hand-In HW # 3
Spring 2013-Rimmer
Spring 2005
Name___________________________________
Recitation Number _________________________
University of Pennsylvania
Math 114 Spring 2013 Final Exam
Powers, Donagi, Rimmer, and Lieberman
1. Assume the acceleration of gravity is 10 m/sec 2 downwards. A cannonball is fired at ground level. If
the cannon ball rises to a height of 80 meters and travels a distance of 240 meters before it hits the
ground, what is the magnitude of the initial velocity in meters per second?
(A) 36
(B) 48
(C) 50
(D) 54
(E) 60
(F) 64
(G) 72
(H) 80
(I) None of the above
2. Find the equation of the plane that passes through (1,3, 2 ) and contains the line
x = 1 + t
y = −1 − 2t
z = 3 + 2t
The y-coordinate of the point where this plane intersects the y − axis is
(A) -1
(B) 0
(C) 1
(D) 2
(E) 3
(F) 4
(G) 5
(H) 6
(I) None of the above
University of Pennsylvania
Math 114 Spring 2013 Final Exam
3. Find the curvature for r ( t ) = −t , − ln ( cos t ) , 0 at t =
Powers, Donagi, Rimmer, and Lieberman
π
4
.
(A) 1
(B) 2
(C) 2
(D) 2 2
(E)
2
2
(F)
3
2
(G) 3 2
(H)
2
3
(I) None of the above
4. Find the arclength of the vector function
r ( t ) = 3cos t i + 3sin t j + 2t 3/ 2 k
for 0 ≤ t ≤ 3.
(A) 12
(B) 14
(C) 16
(D) 18
(E) 20
(F) 24
(G) 28
(H) 32
(I) None of the above
1
University of Pennsylvania
Math 114 Spring 2013 Final Exam
Powers, Donagi, Rimmer, and Lieberman
5. Let
r ( t ) = 2 cos t i + 2 sin t j + t k
Using the parametric equations for the line tangent to the function at t =
π
4
, find the coordinates of
the point where the tangent line intersects the xy − plane.
(A) (1,1, 0 )
(B) (1, −1, 0 )


π


π
(C) 1 −
(D) 1 +
4
4
,1 +
,1 −

,0
4 
π

,0
4 
π
π
π

− 1, + 1, 0 
2
2

(E) 


(F) 1,1,
(G)
π

4
( 0, 0, 0 )
(H) The line does not intersect the xy − plane.
(I) None of the above
6. Let z = x y + x and x = 2 s + t , y = s 2 − 7t. Find
(A)
(B)
(C)
(D)
(E)
−22
3
−7
−8
−20
3
−23
3
∂z
when s = 4 and t = 1.
∂t
−25
3
(G) −9
−31
(H)
3
(F)
(I) None of the above
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