Practice variation 1 of 3
Vector motion — Collision with $\tan\theta=2$
Your question
Particle A is projected from the origin with speed at angle to the horizontal. Particle B is projected horizontally with speed from height above the origin at the same instant. Position vectors: , . Given and the particles collide:
(i) By first showing , verify that .
(ii) Hence show that the particles collide at time .
(iii) When they collide their velocity vectors are perpendicular. Show that .
(iv) Hence find the maximum height of A's parabolic 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?