20 Two particles \(P\) and \(Q\) are moving in separate straight lines across a smooth horizontal surface.
\(P\) moves with constant velocity \(( 3 \mathbf { i } + 4 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\)
\(Q\) moves from position vector \(( 5 \mathbf { i } - 7 \mathbf { j } )\) metres to position vector \(( 14 \mathbf { i } + 5 \mathbf { j } )\) metres during a 3 second period.
20
- Show that \(P\) and \(Q\) move along parallel lines.
20 - Stevie says
Q is also moving with a constant velocity of \(( 3 \mathbf { i } + 4 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\)
Explain why Stevie may be incorrect.
[0pt]
[1 mark]
Question 20 continues on the next page
20 - A third particle \(R\) is moving with a constant speed of \(4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), in a straight line, across the same surface.
\(P\) and \(R\) move along lines that intersect at a fixed point \(X\)
It is given that:
- \(P\) passes through \(X\) exactly 2 seconds after \(R\) passes through \(X\)
- \(P\) and \(R\) are exactly 13 metres apart 3 seconds after \(R\) passes through \(X\)
Show that \(P\) and \(R\) move along perpendicular lines.