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← 2021 HSC Extension 1 paper Question 13(b)

Variation 3 · answer guide

Vector motion — Ceiling check with different angle

Question

With , , room height , find the largest so that max height equals .

This practice question was inspired by Question 13(b) in the 2021 NSW HSC Mathematics Extension 1 examination, © NESA. It is an original TestMum variation that practises the same mathematical idea, not an official NESA question.

Step by step

  1. Set up the solution: differentiate position to get velocity and acceleration, then translate the angle condition into a dot product.At max: .
  2. Simplify the previous line carefully, keeping exact values where possible..
  3. Finish the calculation, then check that the result meets the question’s conditions..
  4. State the final answer clearly in the form the question requested..

Common mistake: changing so many features that the new example no longer tests the same mathematical idea.

Verification: Any larger would hit a ceiling.

Any mark labels are a TestMum study aid, not an official NESA marking allocation.

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