- \hspace{0pt} [In this question the unit vectors \(\mathbf { i }\) and \(\mathbf { j }\) are due east and due north respectively.]
A stone slides horizontally across ice.
Initially the stone is at the point \(A ( - 24 \mathbf { i } - 10 \mathbf { j } ) \mathrm { m }\) relative to a fixed point \(O\).
After 4 seconds the stone is at the point \(B ( 12 \mathbf { i } + 5 \mathbf { j } )\) m relative to the fixed point \(O\).
The motion of the stone is modelled as that of a particle moving in a straight line at constant speed.
Using the model,
- prove that the stone passes through \(O\),
- calculate the speed of the stone.