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1 KINEMATICS P10 007 There are two aircraft flying over Sydney,
an Airbus 320 and Boeing 787. With respect to the ground and Sydney Airport
as the Origin, the displacements (measured from Origin) and the velocities of
the planes at time t =
0 s are Airbus:
displacement
8.56 km 43.5o
S of W velocity 400 km.h-1 37.2o S of E Boeing:
displacement
5.30 km 23.5o
N of E velocity 300 km.h-1 63.2o N of E Calculate
the following at time t =
0 and show graphically all vector quantities: A The distance separating the Airbus and
Boeing. B The displacement of the Airbus w.r.t.
(with respect to) to the Boeing C The displacement of the Boeing w.r.t Airbus. D The relative speed of the Airbus w.r.t.
Boeing. E The relative speed of Boeing w.r.t
Airbus. F
The velocity of Airbus w.r.t Boeing. G The velocity of Boeing w.r.t Airbus. The
two planes are both flying horizontally at constant velocities. H Repeat the above calculations after a
time interval of 12 minutes (t =
12 min).
This
is a long question, much longer than you would get in an exam. However, if
you can do this problem, you will be able to solve virtually all relative motion
problems you are likely to encounter. Remember, the reason you do any
problems is to improve your knowledge and conceptual understanding of your
physics. You goal in doing this question is not necessarily getting the
correct answers, but improving your problem solving
skills. The question is really all about vectors. You should always write down
(or think about it) what you know, before you start answering the question.
So, in the is question, identify the Systems and Events and all the vectors
quantities. A vector is fully specified
by: its magnitude, direction, X and Y components and can be expressed in
terms of the unit vectors. Do this for each vector.
For
relative motion, we often need to add to subtract vectors.
View solution below only after you have completed the answering
the question. |
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Solution We need to specify the vectors for
displacement and velocity in terms of their X and Y components. Let the frame
of reference be the XY plane with the Origin at Sydney Airport. All angles
are measured w.r.t the X axis from -180o to +180o.
Let System A be the Airbus plane and System B be
the Boeing plane.
The boxes in the graph indicate the X and Y
components of each vector. A The distance separating the Airbus and
Boeing.
B The displacement of the Airbus w.r.t. to
the Boeing.
C The displacement of the Boeing w.r.t
Airbus.
D The relative speed of the Airbus w.r.t.
Boeing. E The relative speed of Boeing w.r.t
Airbus. The
relative speeds must be the same. F The velocity of Airbus
w.r.t Boeing.
G The velocity of Boeing w.r.t Airbus.
The
two planes are both flying horizontally at constant velocities. H Repeat the above calculations after a
time interval of 10 minutes (t =
12 min). Since,
the velocities of the two planes are constant, the velocities of the planes
and relative velocities of the planes do not change in the 12
min interval. So, the numerical answers to D E F G are the same. The
velocities do not depend upon the separation distance of the two planes. Event
#1 corresponds to the positions and velocities of the two planes at time t
= 0. Event #2 corresponds to the positions of the velocities of
the two planes at time t =
12 min = (1/5) hour. For Event #2, the displacements of the planes are given
by:
Event
#2 Displacement
of Airbus w.r.t Boeing (AB)
Event
#2 Displacement
of Boeing w.r.t Airbus (BA)
Remember:
Angles all measured with respect to +X axis |
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