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FACULTY OF SCIENCE
FINAL EXAMINATION
PHYS 230
DYNAMICS OF SIMPLE SYSTEMS
Examiner: Prof. R. Harris
Friday December 8th, 2006
Associate Examiner: Prof. N. de Takacsy
2:00  5:00 pm
INSTRUCTIONS:
Answer all questions in the booklet provided. There are 5 questions at 10 points
each.
Textbooks and/or notes are not permitted. However, calculators are permitted,
and formulae are provided on the last page. Dictionaries, if required, are also
permitted.
You may keep the question paper.
This exam comprises 5 pages, with questions on pages numbered 1 through 3.
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View Full DocumentPHYS 230
1
1.
This problem was provided as an “extra” before the MidTerm.
Two boats are playing on a lake – or, rather, their drivers are playing. One boat, “Albert”,
is traveling due East (left to right), and the second, “Brigitte”, starts 500 metres to the
North, and tries to meet up with the ﬁrst.

?
w
w
Albert
Brigitte
There are three scenarios. In all three, Albert always travels due East. At the beginning
of each scenario, Albert is always travelling at 4 m/s, and Brigitte at 5 m/s. Take the
origin of coordinates to be the original position of Albert.
In each scenario,
Brigitte always attempts to travel directly towards Albert, so
as to meet in the shortest possible time.
.
You are advised to solve all three scenarios by working in Brigitte’s frame of
reference
: this should make the solution(s) easier.
(a) Albert has constant
velocity
4 m/s due East, Brigitte has constant
velocity
5 m/s.
Show that, in order that they meet, Brigitte must travel at an angle
θ
= arccos (4
/
5)
South of East.
In Brigitte’s frame, Albert will always be travelling towards her. This means that she
will always match the component of his velocity that is perpendicular to the line from
her to him.
Therefore, the component of her velocity to the East must be 4 m/s. And, conse
quently, the component of her velocity to the South must be 3 m/s, so that she travels
at an angle
θ
= arccos (4
/
5)
South of East.
Z
Z
Z
Z
Z~
?

4
5
3
What is the time and place of the meeting?
In her frame, he has to travel a distance of 500 m with a velocity of 3 m/s. This
takes 500/3 seconds.
The place of meeting is
500
/
3
×
4
±
667
metres to the East of Albert’s initial position.
(b) Albert now accelerates at 0.01 m/s
2
, starting at 4 m/s due East, and in response,
starting at 5 m/s, in the direction
θ
= arccos (4
/
5) South of East, Brigitte accelerates
at 0.0125 m/s
2
.
What is the time and place of the meeting?
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