4 A particle is projected from a point \(O\) on horizontal ground with speed \(50 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at an angle \(\theta\) to the horizontal. Given that the speed of the particle when it is at its highest point is \(40 \mathrm {~m} \mathrm {~s} ^ { - 1 }\),

1. show that \(\cos \theta = 0.8\),
2. find, in either order,
   (a) the greatest height reached by the particle,
   (b) the distance from \(O\) at which the particle hits the ground.