Practice variation 3 of 3
Vector motion — Collision with $\tan\theta=4$
Your question
Same projection setup. Given and the particles collide:
(i) Show and hence .
(ii) Hence show the collision time is .
(iii) Velocities are perpendicular at collision. Taking the earlier collision time, show .
(iv) Hence express the vertex height of A's trajectory 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?