HP 39gs Master Guide

Example 2
Two ships are traveling according to the vector motions given below, where time is in hours and
distance in kilometers. Illustrate their motion during the first ten hours.
⎛
−
100
⎞⎛
20
⎞
Ship A
:
x

=
⎜
+ t
A
⎟⎜ ⎟
⎝
500
⎠⎝
−
30
⎠
⎛
200
⎞⎛
−
15
⎞
Ship B
:

= +
t
x
B
⎜⎟⎜ ⎟
⎝
400
⎠⎝
−
20
⎠
Enter the equations of motion as shown right.
Now change to the
PLOT SETUP view and set the axes to suitable
values. Possible values are shown below.
Now press
PLOT to see the ships paths appear. As with the previous
example, the value of
TStep is chosen to allow visible motion. As the
graph appears it can be seen that the ships do not collide, even though
the final plot may make it appear that they do.
To find the distance between the two ships at any time t, you can enter
X
2
X
2
the equation
F1(X)=
(
X1
()
− X 2
())
+
(
Y X X 1
()
− Y 2
())
into the
Function aplet. Note that the active variable must be an X in the Function
aplet instead of the T of the Parametric aplet but you can still refer to the
Parametric functions
X1 and Y1 even within the Function aplet. Graphing
this function in the
PLOT view of the Function aplet will allow you to find
its minimum value. In this case the minimum separation of 13.74 km is
achieved at t=8.68 hrs.
97

HP 39gs Specifications

General

Type	Scientific
Form factor	Pocket
Product color	Gray
Internal memory	0.256 MB

Weight and Dimensions

Weight	249 g
Dimensions (WxDxH)	187 x 94 x 31 mm