4020 A$ = "@SOME THINGS YOU SHOULD HAVE NOTICED IN THIS EXAMPLE ARE:": GOSUB 10000
4030 VT = VT +1
4040 A$ = "1. @THE BALL TOOK THE SAME TIME TO GO UP AS IT DID TO GO DOWN.": GOSUB 10000
4050 A$ = "2. @THE VELOCITY CHANGED FROM POSITIVE TO NEGATIVE AT THE HIGHEST POINT (IT WAS ACTUALLY ZERO AT THIS POINT)."
4060 GOSUB 10000:VT = VT +1
4070 A$ = "@NOW LET'S USE THESE TWO FACTS TO COMPUTE THE ANSWER TO A VERY SIMPLE PROBLEM.": GOSUB 10000
4080 GOSUB 15000
4090 V0 = ( INT( RND(8) *10) +1) *10
4100 CENTER = 1
4110 A$ = "@PROBLEM 1": GOSUB 10000
4120 CENTER = 0
4130 A$ = "@A TENNIS BALL IS THROWN DIRECTLY UPWARDS WITH AN INITIAL VELOCITY OF " + STR$(V0) +" M/SEC. @HOW HIGH (IN METERS) WILL IT GET BEFORE IT BEGINS TO FALL BACK TOWARDS THE @EARTH?": GOSUB 10000
4140 VT = VT +1
4150 A$ = "@ENTER YOUR ANSWER OR '@H' IF YOU NEED HELP.": GOSUB 10000
4160 GOSUB 17000
4170 IF LEFT$(G$,1) < >"H" THEN 4310
4180 HGR2 :VT = 1
4190 A$ = "@TO COMPUTE THE ANSWER TO THIS PROBLEM, FIRST USE THE FACT THAT THE VELOCITY IS ZERO AT THE HIGHEST POINT.": GOSUB 10000
4200 A$ = "@USE THE EQUATION: V=GT+VO AND SOLVE FOR T.": GOSUB 10000
4210 A$ = "@THIS IS THE TIME AT WHICH THE BALL REACHES ITS HIGHEST POINT.": GOSUB 10000
4220 A$ = "@NOW SUBSTITUTE INTO THE EQUATION:": GOSUB 10000
4230 CENTER = 1
4240 A$ = "S=1/2 GT + V T": GOSUB 10000
4250 VT = VT -3
4260 A$ = " 2 ": GOSUB 10000
4270 A$ = " O ": GOSUB 10000
4280 CENTER = 0
4290 A$ = "@HOW HIGH (IN METERS) DOES THE BALL GET WITH AN INITIAL VELOCITY OF " + STR$(V0) +" M/SEC?": GOSUB 10000
4300 GOSUB 17000
4310 HGR2 :VT = 1
4320 AN = VAL(G$)
4330 V = 0
4340 T = (V -V0)/G
4350 S = 1/2 *G *T *T +V0 *T
4360 S = INT(S *10 +.5)/10
4370 IF ABS(S -AN) <.6 THEN 4410
4380 A$ = "@SORRY, THAT'S NOT CORRECT.": GOSUB 10000
5000 REM <CTRL-J><CTRL-J>HORIZONTAL COMPONENT<CTRL-J>
5010 A$ = "@NOW LET'S EXAMINE THE HORIZONTAL COMPONENT OF PROJECTILE MOTION.": GOSUB 10000
5020 CENTER = 1:VT = VT +1
5030 A$ = "PROBLEM 2": GOSUB 10000
5040 CENTER = 0
5050 A$ = "@A SPACESHIP IS TRAVELLING AT 1000 M/SEC IN A FRICTIONLESS ENVIRONMENT. @AT WHAT TIME WILL IT STOP?": GOSUB 10000
5060 GOSUB 17000
5070 IF G$ < >"H" THEN 5100
5080 A$ = "@NO HINTS ON THIS PROBLEM!": GOSUB 10000
5090 GOSUB 17000
5100 HGR2 :VT = 1
5110 IF LEFT$(G$,8) = "IT WON'T" THEN 5190
5120 IF LEFT$(G$,11) = "IT WILL NOT" THEN 5190
5130 IF LEFT$(G$,13) = "IT WILL NEVER" THEN 5190
5140 IF LEFT$(G$,5) = "NEVER" THEN 5190
5150 IF LEFT$(G$,10) = "AT NO TIME" THEN 5190
5160 IF ASC(G$) >47 AND ASC(G$) <58 THEN 5210
5170 A$ = "@I CAN'T FIGURE OUT WHAT YOUR ANSWER IS, BUT THE CORRECT ANSWER IS THAT IT WILL NEVER STOP!": GOSUB 10000
5180 GOTO 5230
5190 A$ = "@THAT'S CORRECT!": GOSUB 10000
5200 GOTO 5230
5210 A$ = "@THAT'S NOT CORRECT. @THE SPACESHIP WILL NEVER STOP.": GOSUB 10000
5220 GOTO 5230
5230 VT = VT +1
5240 A$ = "@THIS IS WHY YOU WILL HAVE TO FIND THE TIME THAT A PARTICLE STOPS BY USING THE VERTICAL COMPONENT, AND THEN USING THAT TIME IN THE HORIZONTAL COMPONENT FORMULA.": GOSUB 10000
5250 GOSUB 15000
5260 RETURN
6000 REM <CTRL-J><CTRL-J>HORIZONTAL PROBLEM<CTRL-J>
6010 A$ = "@HERE IS A BRIEF DEMONSTRATION PROBLEM TO ILLUSTRATE HOW TO SOLVE PROJECTILE MOTION PROBLEMS.....": GOSUB 10000
6020 VT = VT +1
6030 A$ = "@A BALL IS FIRED FROM A CANNON WITH AN INITIAL VELOCITY OF 30 M/SEC AND AN ANGLE OF INCLINATION OF 45" + CHR$(2) +". @HOW HIGH WILL THE BALL GET, AND HOW FAR AWAY WILL IT LAND.": GOSUB 10000
6040 GOSUB 15000
6050 A$ = "@FIRST, WE HAVE TO FIGURE OUT THE HORIZONTAL AND VERTICAL COMPONENTS FROM THE GIVEN DATA. @THE FORMULAS THAT HAVE TO BE USED TO DO THIS ARE:": GOSUB 10000
6060 CENTER = 1
6070 A$ = "V = V @C@O@S @A": GOSUB 10000
6080 VT = VT -1
6090 A$ = " H O ": GOSUB 10000
6100 A$ = "V = V @S@I@N @A": GOSUB 10000
6110 VT = VT -1
6120 A$ = " V O ": GOSUB 10000
6130 CENTER = 0
6140 A$ = "@WHEN WE PUT THE GIVEN INFORMATION INTO THESE FORMULAS, WE GET...": GOSUB 10000
6420 A$ = "@THIS MEANS THAT AT " + STR$(T) +" SECONDS, THE BALL IS AT ITS HIGHEST POINT.": GOSUB 10000
6430 GOSUB 15000
6440 A$ = "@WE NOW INSERT THIS INTO THE EQUATION:": GOSUB 10000
6450 CENTER = 1
6460 A$ = "S = 1/2 GT + V T": GOSUB 10000
6470 VT = VT -3
6480 A$ = " 2 ": GOSUB 10000
6490 A$ = " V ": GOSUB 10000
6500 CENTER = 0
6510 S = 1/2 *G *T *T +VV *T
6520 S = INT(S *10 +.5)/10
6530 A$ = "AND WE GET HEIGHT = " + STR$(S): GOSUB 10000
6540 A$ = "@THIS IS THE ANSWER TO THE FIRST PART.": GOSUB 10000
6550 VT = VT +1
6560 A$ = "@THE SECOND PART IS EASY NOW. @SINCE IT TAKES " + STR$(T) +" SECONDS TO GO UP, IT MUST ALSO TAKE " + STR$(T) +" SECONDS TO GO DOWN, SO IT WILL HIT THE GROUND AT " + STR$(T *2) +" SECONDS.": GOSUB 10000
6570 GOSUB 15000
6580 RETURN
7000 REM <CTRL-J><CTRL-J>SECOND PART OF PROBLEM<CTRL-J>
7010 T = T *2
7020 A$ = "@USING THE EQUATION:": GOSUB 10000
7030 CENTER = 1
7040 A$ = "S = V T": GOSUB 10000
7050 VT = VT -1
7060 A$ = " H ": GOSUB 10000
7070 CENTER = 0
7080 S = VH *T
7090 A$ = "WE FIND THAT AT " + STR$(T) +" SECONDS, THE BALL HAS TRAVELLED " + STR$(S) +" METERS. @THIS IS THE ANSWER TO THE SECOND PART.": GOSUB 10000
7100 VT = VT +1
7110 A$ = "@HERE IS A DEMONSTRATION OF THIS MOTION. @NOTICE HOW IT CONFORMS TO OUR INFORMATION.": GOSUB 10000
7120 GOSUB 15000
7130 RETURN
8000 REM <CTRL-J><CTRL-J>SET UP GRID<CTRL-J>
8010 HCOLOR= 3
8020 HPLOT 5,0 TO 5,183 TO 279,183
8030 FOR X = 0 TO 91
8040 Y1 = 187
8050 IF X/5 = INT(X/5) THEN Y1 = 189
8060 IF X/10 = INT(X/10) THEN Y1 = 191
8070 HPLOT X *3 +5,183 TO X *3 +5,Y1
8080 NEXT X
8090 FOR Y = 0 TO 60
8100 X1 = 2
8110 IF Y/5 = INT(Y/5) THEN X1 = 1
8120 IF Y/10 = INT(Y/10) THEN X1 = 0
8130 HPLOT 5,183 -Y *3 TO X1,183 -Y *3
8140 NEXT Y
8150 RETURN
8200 REM <CTRL-J><CTRL-J>CONTROL THROWING OF BALL<CTRL-J>