Collisions & closest approach
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Flip to reveal answersWhat must be true for two objects to collide?
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All 8 Flashcards — Collisions & closest approach
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Question
What must be true for two objects to collide?
Answer
They must be at the SAME position at the SAME value of t — one t satisfies every coordinate of r_A(t) = r_B(t).
Question
Why isn't 'paths crossing' the same as a collision?
Answer
Two objects can pass through the same point at different times; a collision needs the same point at the same moment.
Question
How do you check for a collision?
Answer
Set r_A(t) = r_B(t), solve one coordinate for t, then CHECK that t in the other coordinate(s). If it fits all, they collide.
Question
How do you find the distance between two moving objects?
Answer
d(t) = |r_B(t) − r_A(t)| = √((Δx)² + (Δy)²), the length of the displacement between them.
Question
How do you find the closest approach?
Answer
Find the MINIMUM of d(t) — graph d(t) on the GDC and read the lowest point (x = time, y = least distance).
Question
Why can you minimise d(t)² instead of d(t)?
Answer
d(t) is least exactly where d(t)² is least (both positive, square root is increasing), and d² has no awkward square root.
Question
What does the minimum point of d(t) tell you?
Answer
Its x-coordinate is the time of closest approach; its y-coordinate is the least distance between the objects.
Question
After finding the least distance, what should you do in an AI HL answer?
Answer
Interpret in context — compare it to the required safety/separation distance and state whether the rule is met.
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Full study notes for Collisions & closest approach
Topic 3.12 hub
Vectors & kinematics (HL only)
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