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Ship A is currently at position vector 21i + 21j km and is currently
travelling at a velocity of -4i + 6j km/hr. Ship B is at 30j and travelling
at 2i + 3j km/hr. If the ships continue on their present courses, show
that they will not collide and find the distance between them at the
time of their closest approach.
Firstly enter the equations for the ships' paths
into the Parametric aplet using the first
equation pair for ship A and the second for
ship B.
Making a guess at the ships' behavior and
position, I will set up the axes as shown on the
right. I am assuming that the collision will
occur in the first 6 seconds and in the axes
range chosen. This can always be adjusted if
my guess is wrong. The reason for choosing -
15 on the YRng is to ensure that the x axis is
visible on the screen. Notice in the second
screen that Simult: must be checked if the plot
is to be a good illustration of the ship's
movements.
If you've done this correctly then you will see
the ship's movements on the plot view. Careful
examination of the paths of the ships as they
appear on the screen will show visibly that they
do not collide. The graph is shown on the right
just before closest approach. However we
need to verify this.
The formula for the distance between the ships
(
) (
is
=
−
2
+
d
x
x
y
1
2
1
entered into the Function aplet as shown right.
With an equation this complex it is probably
worth checking with the
have typed it correctly. Notice that the active
variable in Function must be X not the T used
in Parametric.
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and this can now be
−
2
y
2
key that you
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