Case study·Hard exam skill (4/5)·No calculator
Difficulty guide
The label describes the problem, not your ability.
1/5 - Foundational
Warm-up setup; checks one basic idea.
2/5 - Routine exam skill
Normal syllabus skill; usually one main rule or interpretation.
3/5 - Standard multi-step
Exam-style problem with multiple steps or a common trap.
4/5 - Hard exam skill
High-end exam problem; combines methods carefully.
5/5 - Challenge
Stretch problem beyond normal exam pressure.
Question
A boat must cross a wide river and reach the point directly opposite its start. The river current is downstream, and the boat's speed relative to water is . The boat is aimed upstream at a fixed angle to the straight-across direction.
Total: 5 marks
(a) Find the upstream component of the boat's velocity relative to water. (1 mark)
(b) Find the component of the boat's velocity straight across the river. (2 marks)
(c) Find the crossing time. (1 mark)
(d) Find the angle between the boat's heading and the straight-across direction. (1 mark)
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