Specialist2025 Exam 1 · Q5Tech-free4 marks

Colliding particles with perpendicular velocities

The position vectors of particles $P$ and $Q$ at time $t$ seconds are given by

${\underset{\sim}{r}}_{P} (t) = (t^{3} + a t^{2}) \underset{\sim}{i} - \underset{\sim}{j} and {\underset{\sim}{r}}_{Q} (t) = (b t + 2 t) \underset{}{i}$

Show that for collision to occur when $t = 1$ , the value of $c$ is $-4$ .

1 mark

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When the particles collide, their velocities are at right angles to each other.

Find the two possible values of $a$ for collision to occur when $t = 1$ .

2 marks

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When the particles collide at $t = 1$ , the magnitudes of their accelerations are equal.

Find the values of $a$ and $b$ for collision to occur when $t = 1$ .

1 mark

Hints, answer checking and worked solutions come with a Season Pass.