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PHCC 141: Physics for Scientists and Engineers I  Fall 2007
3b. Motion in Two or Three Dimensions (long/challenging start early!)
Due at 11:59pm on Monday, September 10, 2007
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Number of answer attempts per question is:
5
You gain credit for:
correctly answering a question in a Part, or correctly answering a question in a Hint.
You lose credit for:
exhausting all attempts or requesting the answer to a question in a Part or Hint, or incorrectly answering a question in a Part.
Late submissions:
reduce your score by 100% over each day late.
Hints
are helpful clues or simpler questions that guide you to the answer. Hints are not available for all questions. There is
no penalty
for leaving questions in Hints unanswered.
Grading of
Incorrect Answers
For
MultipleChoice
or
True/False
questions, you lose
100%
/
(
# of options  1
)
credit per incorrect answer.
For
any other
question, you lose 3% credit per incorrect answer.
Standard projectile problems
Shooting over a Hill
A projectile is fired with speed
at an angle
from the horizontal as shown in the figure .
Part A
Find the highest point in the trajectory,
.
Hint A.1
Velocity at the top
Hint not displayed
Hint A.2
Which equation to use
Hint not displayed
Express the highest point in terms of the magnitude of the acceleration due to gravity
, the initial velocity
, and the
angle
.
ANSWER:
=
Part B
What is the range of the projectile,
?
Part B.1
Find the total time spent in air
Part not displayed
Part B.2
Find
Part not displayed
Express the range in terms of
,
, and
.
ANSWER:
=
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Consider your advice to an artillery officer who has the following problem. From his current postition, he must shoot over a hill
of height
at a target on the other side, which has the same elevation as his gun. He knows from his accurate map both the
bearing and the distance
to the target and also that the hill is halfway to the target. To shoot as accurately as possible, he
wants the projectile to just barely pass above the hill.
Part C
Find the angle
above the horizontal at which the projectile should be fired.
Hint C.1
How to approach the problem
In the first half of this problem, you found
and
in terms of
and
. Solve these two equations to find
in terms of
and
.
Part C.2
Set up the ratio
Find the ratio of
to
.
The only variable in your answer should be
.
ANSWER:
=
Express your answer in terms of
and
.
ANSWER:
=
Recall the following trigonometry formulas:
,
,
and
.
In this case, since
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