5 The equation of the trajectory of a small ball \(B\) projected from a fixed point \(O\) is $$y = - 0.05 x ^ { 2 }$$ where \(x\) and \(y\) are, respectively, the displacements in metres of \(B\) from \(O\) in the horizontal and vertically upwards directions.

1. Show that \(B\) is projected horizontally, and find its speed of projection.
2. Find the value of \(y\) when the direction of motion of \(B\) is \(60 ^ { \circ }\) below the horizontal, and find the corresponding speed of \(B\).
   \(6 \quad O , A\) and \(B\) are three points in a straight line on a smooth horizontal surface. A particle \(P\) of mass 0.6 kg moves along the line. At time \(t \mathrm {~s}\) the particle has displacement \(x \mathrm {~m}\) from \(O\) and speed \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The only horizontal force acting on \(P\) has magnitude \(0.4 v ^ { \frac { 1 } { 2 } } \mathrm {~N}\) and acts in the direction \(O A\). Initially the particle is at \(A\), where \(x = 1\) and \(v = 1\).
3. Show that \(3 v ^ { \frac { 1 } { 2 } } \frac { \mathrm {~d} v } { \mathrm {~d} x } = 2\).
4. Express \(v\) in terms of \(x\).
5. Given that \(A B = 7 \mathrm {~m}\), find the value of \(t\) when \(P\) passes through \(B\).