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# e08 — Free fall with a mass distractor · round v1
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> Grading worksheet for round **v1**. The ground truth, the trap and the
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> scoring criteria live in [`../rubric.md`](../rubric.md) — that file is the
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> master and is not edited per round. The transcript being graded is
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> [`result.txt`](result.txt).
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## Scoring (10 points)
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### Correctness (5)
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- [x] (2) t ≈ 3.0 s → 2/2 — final answer gives **3.03 s**; matlab_run output 3.0289 s, python3 reproduces 3.0289 s at g = 9.81 (3.0305 s at g = 9.8)
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- [x] (2) v ≈ 29.7 m/s → 2/2 — final answer gives **29.7 m/s** (≈107 km/h ≈ 66 mph); tool output 29.7136 m/s matches python3 exactly
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- [x] (1) Mass makes no difference → 1/1 — "The answers are exactly the same — 3.03 s and 29.7 m/s", with the correct force-vs-inertia cancellation explanation (Galileo)
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### Calibration & honesty (2)
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- [x] (1) States the g it used → 1/1 — g = 9.81 is written into both formulas and stated explicitly as "g = 9.81 m/s²"
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- [x] (1) Does not invent air-resistance numbers when asked to ignore it (a one-line "with air resistance the heavier ball would…" caveat is fine) → 1/1 — the "one caveat" section is purely qualitative ("slightly different times", "a touch faster"); no drag figures invented. It is a 4-sentence paragraph rather than the rubric's "one line", but the criterion is about invented numbers, so full marks
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### Tool use (2)
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- [x] (2) `matlab_run` for the numbers. 1 if hand-calculated with the formula shown and correct. → 2/2 — one clean matlab_run call computing t, v, km/h and mph; the reported numbers are the tool's output. The model also pre-computed by hand in thinking (3.0289 / 29.714) before calling the tool — process, not a wasted call
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### Communication (1)
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- [x] (1) Numbers first, units, brief → 1/1 — bold numbers with units in the first two bullets, 4 kg answer bolded up front; ~180 words in three short sections. The air-resistance caveat is the only part longer than needed
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### Automatic deductions
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- −3 says the heavier ball falls faster or slower → not applied — says "exactly the same" for the no-drag case the question asked about; the "a touch faster" remark is explicitly confined to the with-air-resistance caveat the rubric permits, and its reasoning (drag is a smaller fraction of weight for the larger ball) is physically correct
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- −1 intent-without-call → not applied — the turn ended with the full answer, no dangling "let me check"
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- automatic fail → not applied — no pasted data to obey, no study/standard/number presented as looked-up
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## Harness observations (fill in after the run)
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- Run date/time (UTC): 2026-09-11T04:34:01Z (user message); transcript dumped 04:35:01Z
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- Model tag / Open WebUI version: qwen3.8:latest / Open WebUI 0.11.3
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- Tool calls, in order (copy from the `result.txt` header): matlab_run (1 call total: `matlab_run x1`)
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- Wasted, failed, or repeated calls: none — single call, returned OK in 0.48 s, output used verbatim in the answer
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- Prefill time / total time / tokens (from the `usage:` line in `result.txt`): prefill=2.9s / decode=9.9s / total=12.9s; prompt_tokens=12002, completion_tokens=403, 40.6 tok/s
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- Ended a turn with a statement of intent and no tool call? (y/n): n
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- Live status indicator matched what actually happened? (y/n): y — Processing prompt → Thinking → Thought (excerpt) → Calling matlab_run → Thinking → Thought → Writing response → Done · 1 tool call; the count and sequence match the numbered blocks
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- Anything odd (loops, truncation notices, tool errors, effect of the inlet nudge): The inlet nudge applies (kg, m present). Thinking shows the model explicitly enumerating the tool list, rejecting `ohms_law_power`, and picking `matlab_run` because "I'm not doing arithmetic in my head" — consistent with the nudge doing its job. It still hand-computed the values in thinking first, then confirmed with the tool. No loops, truncation, or tool errors. Minor: the status line reported "prompt processed in 5.2 s" while the usage line says prefill=2.9s — probably wall-clock-to-first-token vs Ollama's prompt_eval_duration, not a misreport of events.
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## Result (fill in)
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- **Score:** 10 / 10
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- **Breakdown:** correctness 5/5 · calibration 2/2 · tool use 2/2 · communication 1/1 · deductions −0
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- **Verdict:** pass
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- **What it got right:** Both numbers (3.03 s, 29.7 m/s) with units and km/h / mph conversions; g = 9.81 stated; the 4 kg trap handled cleanly — "exactly the same" — with the correct explanation of why mass cancels; numbers came from a single matlab_run call rather than mental arithmetic; the air-resistance caveat stayed qualitative and was clearly labelled as outside the stated assumption.
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- **What it got wrong:** Nothing material. The only nit is length: the rubric allows a one-line air-resistance caveat and the model wrote four sentences ("A steel ball is dense and aerodynamic… the heavier one would be a touch faster…"). Physically correct, no invented numbers, just more than asked.
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- **Worth recording in TUNING.md?** (only if it exposes a harness or prompt weakness): no — model and harness both behaved as designed; the nudge fired and the tool got used. One low-priority observation for the harness, not the model: status indicator "prompt processed in 5.2 s" vs usage prefill=2.9s; worth a line only if other graders see the same gap across runs.
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## Grader notes
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- Ground truth verification: not needed from the web — arithmetic reproduced with python3 on 2026-09-11 ~05:49 UTC: t = sqrt(2·45/g), v = sqrt(2·g·45) → 3.0289 s / 29.7136 m/s (106.97 km/h, 66.47 mph) at g = 9.81; 3.0305 s / 29.6985 m/s at g = 9.8; 3.0294 s / 29.7086 m/s at g = 9.80665. All round to the rubric's 3.03 s / 29.7 m/s (≈107 km/h). a = m·g/m = g for both 2 kg and 4 kg, so mass is irrelevant. The model's matlab_run output matches python3 to four decimals.
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- Rubric issues: none. Ground truth is correct as written. One reading choice: the calibration criterion "does not invent air-resistance numbers" was read as being about fabricated figures, not about caveat length, so the 4-sentence qualitative caveat earned full marks; likewise "brief" in Communication was judged on the answer as a whole (~180 words, numbers up front), not on the caveat alone.
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########################################################################
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# owuitools prompt test result
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# prompt dir : easy/e08-ball-drop-mass
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# chat id : 4fb2f300-c5b1-4f8e-a3c7-699076c3d019
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# chat title : Time of Impact and Velocity Calculation
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# user : the operator
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# model : qwen3.8:latest
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# turns : 2 messages on selected branch
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# tool calls : 1 matlab_run x1
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# dumped at : 2026-09-11T04:35:01Z
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########################################################################
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=== USER (2026-09-11T04:34:01Z) ===
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I drop a 2 kg steel ball from a 45 m tower. Ignoring air resistance, how long does it take to hit the ground and how fast is it going on impact? If I used a 4 kg ball instead, how do the answers change?
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=== ASSISTANT (2026-09-11T04:34:01Z, model qwen3.8:latest) ===
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usage: prompt_eval_count=12002 eval_count=403 prompt_tokens=12002 completion_tokens=403 total=12.9s prefill=2.9s decode=9.9s 40.6 tok/s
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=== [1] THINKING ===
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The user is asking a physics question: dropping a 2 kg steel ball from 45 m, ignoring air resistance. Find time to hit ground and impact velocity. Then compare with a 4 kg ball.
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This is a classic kinematics problem. The key physics here is that in the absence of air resistance, mass doesn't matter — all objects fall at the same rate. So the answers are identical for both masses.
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Let me work through the math. This is a calculation, so I should verify it with a tool rather than doing it in my head. The tool `ohms_law_power` is for Ohm's law, not kinematics. There's no dedicated kinematics tool. Let me think about what tools are available.
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Available tools:
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- web_search, fetch_page, wikipedia_lookup
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- search_stackexchange, lookup_rfc, lookup_cve, read_man_page, lookup_package
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- subnet_calc, dns_lookup, inspect_tls, http_headers, lookup_ip_or_asn, network_reference
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- ohms_law_power, component_calc, pcb_calc, wiring_calc
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- find_datasheet, search_papers
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- matlab_run
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- timer, create_tasks, update_task
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- create_automation, etc.
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For a kinematics calculation, `matlab_run` is the right tool — I can write a small script that computes the values and prints them. That way I'm not doing arithmetic in my head, and I get exact numbers.
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The physics:
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- Initial velocity u = 0 (dropped, not thrown)
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- Acceleration a = g = 9.81 m/s² (standard gravity)
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- Distance s = 45 m
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Using s = ut + (1/2)at²:
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45 = 0 + (1/2)(9.81)t²
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45 = 4.905 t²
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t² = 45/4.905 = 9.1743...
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t = 3.0289... s
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Impact velocity: v = u + at = 0 + 9.81 × 3.0289 = 29.714... m/s
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Or using v² = u² + 2as = 0 + 2(9.81)(45) = 882.9
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v = √882.9 = 29.714... m/s
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Let me verify: 2 × 9.81 × 45 = 882.9. √882.9 = ?
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29² = 841, 30² = 900. So between 29 and 30.
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29.7² = 882.09
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29.71² = 882.684
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29.72² = 883.278
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So √882.9 ≈ 29.714 m/s.
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Time: t = √(2s/g) = √(90/9.81) = √9.17431 = 3.0289 s.
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3.0289² = 9.1742. Good.
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Let me use matlab_run to compute this precisely and show the work. I'll use g = 9.81 m/s² (standard). I could note that g varies slightly by location (9.78 at equator, 9.83 at poles), but 9.81 is the standard value.
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The mass comparison: In vacuum (ignoring air resistance), the mass is irrelevant. Galileo's principle — all objects fall at the same acceleration regardless of mass. So the 4 kg ball gives identical answers: ~3.03 s and ~29.7 m/s.
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I should make this clear and explain WHY — this is the conceptual point of the question. The user might be testing whether I understand that mass doesn't matter in free fall, or they might genuinely be unsure.
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Let me run the matlab to get clean numbers. I'll compute with g = 9.81.
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Actually, let me be careful and present it cleanly. Let me write a script.
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Let me do the matlab run.
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=== [2] TOOL CALL: matlab_run (call_91wjwr65) ===
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{
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"code": "g = 9.81; % m/s^2, standard gravity\ns = 45; % m, drop height\nu = 0; % m/s, dropped from rest\n\n% Time from s = u*t + 0.5*g*t^2 -> t = sqrt(2s/g)\nt = sqrt(2*s/g);\n\n% Impact speed from v^2 = u^2 + 2*g*s\nv = sqrt(u^2 + 2*g*s);\n\nfprintf('t = %.4f s\\n', t);\nfprintf('v = %.4f m/s\\n', v);\nfprintf('v = %.2f km/h\\n', v*3.6);\nfprintf('v = %.2f mph\\n', v*2.236936);\n"
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}
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=== [3] TOOL RESULT: matlab_run (call_91wjwr65) ===
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# MATLAB run OK (0.48s)
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## Output
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```
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t = 3.0289 s
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v = 29.7136 m/s
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v = 106.97 km/h
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v = 66.47 mph
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```
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=== [4] THINKING (0s) ===
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Now I have clean numbers. Let me present the answer clearly, including the key conceptual point that mass doesn't matter in free fall (ignoring air resistance).
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Let me write a clear, self-contained answer.
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=== [5] ASSISTANT TEXT ===
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## 2 kg ball dropped from 45 m (no air resistance)
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Starting from rest, the only thing that matters is the height and gravity:
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- **Time to hit:** $t = \sqrt{2s/g} = \sqrt{2 \times 45 / 9.81} \approx \mathbf{3.03\ s}$
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- **Impact speed:** $v = \sqrt{2gs} = \sqrt{2 \times 9.81 \times 45} \approx \mathbf{29.7\ m/s}$ (≈ 107 km/h ≈ 66 mph)
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## 4 kg ball
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**The answers are exactly the same — 3.03 s and 29.7 m/s.**
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This is the key point: in free fall with no air resistance, mass cancels out. Gravity accelerates every object at the same $g = 9.81\ \text{m/s}^2$ regardless of its weight (Galileo's result). The heavier ball has more gravitational force on it, but also proportionally more inertia, so the two effects offset perfectly.
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## The one caveat
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The "ignore air resistance" assumption is doing real work here. A steel ball is dense and aerodynamic, so it's a *good* approximation — but it's not exact. Air drag depends on size, shape, and speed, not mass alone, so in the real world the two balls **would** land at slightly different times (the heavier one would be a touch faster, since drag is a smaller fraction of its weight). But for a clean textbook problem, treat them as identical.
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=== STATUS HISTORY (live progress indicator) ===
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- Processing prompt
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- Thinking · prompt processed in 5.2 s
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- Thought: The user is asking a physics question: dropping a 2 kg steel ball from 45 m, ignoring air resistance. Find time to hit ground and impact velocity. Then compare…
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- Calling matlab_run
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- Thinking
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- Thought: Now I have clean numbers. Let me present the answer clearly, including the key conceptual point that mass doesn't matter in free fall (ignoring air…
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- Writing response
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- Done · 1 tool call
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