Practice variation 2 of 3
Vector motion — Collision with $\tan\theta=3$
Your question
Same projection setup as the exam (A from origin at angle , B horizontal from height with speed ). Given and the particles collide:
(i) By first showing , verify that .
(ii) Hence show that the collision time is .
(iii) When they collide their velocities are perpendicular. Show that (taking the earlier collision).
(iv) Hence find the height of the vertex of A's trajectory prior to collision, in terms of .
This practice question was inspired by Question 13(b) in the 2023 NSW HSC Mathematics Extension 1 examination, © NESA. It is an original TestMum variation that practises the same mathematical idea, not an official NESA question.
Before you check
- Have you stated every choice or assumption?
- Can another student follow each line?
- Did you verify the final result independently?