A particle P of mass 0.28 kg is attached to the mid-point of a light elastic string of natural length 4m. The ends of the string are attached to fixed points A and B which are at the same horizontal level and 4.8m apart. P is released from rest at the mid-point of AB. In the subsequent motion, the acceleration of P is zero when P is at a distance 0.7m below AB.

i. Show that the modulus of elasticity of the string is 20N.

ii. Calculate the maximum speed of P.