1. \hspace{0pt} [In this question \(\mathbf { i }\) and \(\mathbf { j }\) are unit vectors in a horizontal and upward vertical direction respectively]

A particle \(P\) is projected from a fixed point \(O\) on horizontal ground with velocity \(u ( \mathbf { i } + c \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\), where \(c\) and \(u\) are positive constants. The particle moves freely under gravity until it strikes the ground at \(A\), where it immediately comes to rest. Relative to \(O\), the position vector of a point on the path of \(P\) is \(( x \mathbf { i } + y \mathbf { j } ) \mathrm { m }\).

1. Show that $$y = c x - \frac { 4.9 x ^ { 2 } } { u ^ { 2 } }$$ Given that \(u = 7 , O A = R \mathrm {~m}\) and the maximum vertical height of \(P\) above the ground is \(H \mathrm {~m}\),
2. using the result in part (a), or otherwise, find, in terms of \(c\),
   1. \(R\)
   2. \(H\). Given also that when \(P\) is at the point \(Q\), the velocity of \(P\) is at right angles to its initial velocity,
3. find, in terms of \(c\), the value of \(x\) at \(Q\).