5 A ball of mass 0.05 kg is released from rest at a height \(h \mathrm {~m}\) above the ground. At time \(t \mathrm {~s}\) after its release, the downward velocity of the ball is \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\). Air resistance opposes the motion of the ball with a force of magnitude \(0.01 \nu \mathrm {~N}\).

1. Show that \(\frac { \mathrm { d } v } { \mathrm {~d} t } = 10 - 0.2 v\). Hence find \(v\) in terms of \(t\).
2. Given that the ball reaches the ground when \(t = 2\), calculate \(h\).