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I want to graph this function for the first six
seconds but I am not sure what y scale to use
so I will set XRng to be 0 to 6 in the PLOT
SETUP view and then choose VIEWS - Auto
Scale. The result is shown right.
Using - Extremum, I find that the time of
closest approach is at t = 3.4 hours (3:24 pm)
with a separation at that time of d = 1.3416
km. The y axis has been adjusted slightly to
make the x axis visible.
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A particle’s position at time t seconds is given by
5sin 5cosri j
θ
−
.
Draw a sketch of its path for the first 6 seconds of movement. Show
algebraically that its path is circular.
The first step is to graph the particle’s path.
We go into the Parametric aplet and enter the
rule into the first equation X1, Y1.
After setting TRng to 0 to 6 and then using
VIEWS - Auto Scale we get a result which is
does not look like a circle, but this may be due
to distortion through not using a ‘square’
screen.
If we inspect the PLOT SETUP
view, we can see that the
settings are nearly double
those of the default ‘square’
screen of -6.5 to 6.5 and -3.1 to 3.2 In the
PLOT SETUP view, press SHIFT CLEAR to set
everything back to default, then double each
setting for the x and y axes and set TRng back
to 0 to 6. Pressing PLOT again will make it
clear visually that this is a circle and we can
copy this diagram onto our test paper as the
required graph. Note the gap at the bottom
because the TRng stops at 6 instead of 2π.
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