3 A small ball of mass \(m \mathrm {~kg}\) is projected vertically upwards with speed \(14 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The ball has velocity \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) upwards when it is \(x \mathrm {~m}\) above the point of projection. A resisting force of magnitude \(0.02 m v \mathrm {~N}\) acts on the ball during its upward motion.

1. Show that, while the ball is moving upwards, \(\left( \frac { 500 } { v + 500 } - 1 \right) \frac { \mathrm { d } v } { \mathrm {~d} x } = 0.02\).
2. Find the greatest height of the ball above its point of projection.