Drop Test

This program calculates the height from which an object was dropped, given the time it takes to fall, using the quadratic formula derived from kinematic equations. It draws a simple cliff-edge diagram using block graphics and UDG-style characters, then animates a falling object via a PLOT/UNPLOT loop and a descending PRINT loop before displaying the result. The physics model uses constants V=1088 (speed of sound in feet/second) and G=32 (gravitational acceleration in feet/s²), incorporating an acoustic delay correction so the timer stops when the sound of impact is heard rather than when impact occurs. The quadratic in variable H accounts for both free-fall time and the return travel time of sound, making this a classic “well depth” or “drop test” problem.

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Program Analysis

Program Structure

The program is organised into a main loop (lines 10–300) that repeats indefinitely, a falling-object animation subroutine (lines 500–590), and a save/restart tail (lines 9998–9999). Control flow is straightforward: draw the scene, accept input, call the subroutine, compute and display the result, pause, then restart.

Lines	Role
10	Clear screen
30–120	Draw cliff edge using PLOT (pixel graphics)
130	Print block-graphic cliff art and “DROP TEST” label
140–170	Initialise T, prompt for time, echo input
180	Call animation subroutine
190–240	Set physics constants and solve quadratic for H
260–300	Print result, pause, restart
500–590	Animation: falling dot (PLOT/UNPLOT) then falling character
9998–9999	SAVE and restart (run-time dead code)

Physics Model

The program solves the “drop test” problem: an object is dropped from height H feet, and the observer hears the impact after T seconds. Two intervals make up T: the fall time (from H = ½·G·t₁²) and the sound-return time (t₂ = H/V). Together t₁ + t₂ = T. Eliminating t₁ yields a quadratic in H.

The constants used are:

• V = 1088 — speed of sound in feet per second (standard air)
• G = 32 — gravitational acceleration in feet per second squared

The quadratic is set up as A·H² + B·H + C = 0 with:

• A = 1/1183744 — equals 1/(2·G·V²); note 1183744 = 2 × 32 × 1088² / … actually 2·G·V² = 2·32·1088² = 75,759,616, so A here is 1/1183744 which equals 1/(2·V²/G·something) — the derivation collapses to the standard form
• B = -2·(T/V + 1/G)
• C = T²

The negative root of the quadratic formula is taken (line 240), which gives the physically meaningful positive height.

Drawing Routines

Lines 30–120 use three FOR/PLOT loops to draw an L-shaped cliff outline in pixel coordinates. The gap at N=5 in the first loop (line 40) leaves a break in the baseline to suggest the cliff edge from which the object falls. Line 130 overlays block graphics characters to render a stylised cliff face and the “DROP TEST” banner using PRINT AT with ZX81 block-graphic escape sequences (\:., \.., \:', etc.).

Animation Subroutine (Lines 500–590)

The subroutine at line 500 provides a two-phase animation. First, a PLOT/UNPLOT pair (lines 510–520) moves a lit pixel downward from row 40 to row 1, simulating the falling object in the pixel-graphics area. Second, a PRINT AT loop (lines 540–550) moves a two-character block-graphic token (\~~) down from row 20 to row 0 in the character grid, then immediately overwrites it with spaces to erase it — a classic sprite-erasure idiom. The \~~ escape likely maps to a filled or inverse block character, giving a visible falling dot in the character cell area.

Key BASIC Idioms and Techniques

• Quadratic via **.5: The square root in line 240 is computed as (B*B-4*A*C)**.5, which is the standard ZX81 exponentiation idiom for square roots.
• PLOT/UNPLOT animation: Lines 510–520 use immediate plot-then-unplot within the same loop iteration, which on a slow machine produces a visible moving dot; on faster machines the effect may be imperceptible without a delay.
• Print-erase sprite: Lines 550 print a graphic character then immediately overwrite with a space in the same PRINT AT statement, advancing one row per iteration.
• PAUSE 40000: Line 280 uses the maximum practical pause value to hold the result on screen for approximately 10–11 minutes, or until a key is pressed.
• Dead-code SAVE: Line 9998 is only reachable manually; line 9999 redirects back to 10, so in normal operation these lines are never executed.