2 As part of a training exercise an army recruit of mass 75 kg falls a vertical distance of 5 m before landing on a mat of thickness 1.2 m . The army recruit sinks a distance of \(x \mathrm {~m}\) into the mat before instantaneously coming to rest. The mat can be modelled as a spring of natural length 1.2 m and modulus of elasticity 10800 N and the army recruit can be modelled as a particle falling vertically with an initial speed of \(2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).

1. Show that \(x\) satisfies the equation \(300 x ^ { 2 } - 49 x - 255 = 0\).
2. Calculate the value of \(x\).
3. Ignoring the possible effect of air resistance, make
   • one comment on the assumptions made and,
   • suggest a possible refinement to the model.