2 A duck of mass 2 kg is travelling with horizontal speed \(4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) when it lands on a lake. The duck is brought to rest by the action of resistive forces, acting in the direction opposite to the duck's motion and having total magnitude \(\left( 2 v + 3 v ^ { 2 } \right) \mathrm { N }\), where \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) is the speed of the duck. Show that the duck comes to rest after travelling approximately 1.30 m from the point of its initial contact with the surface of the lake.