1. The conservation of mechanical energy states that if there are no forces other than gravity acting on a particle during its motion, then the sum of its kinetic and potential energies remains constant.

A brick of mass 5 kg is held at rest 3 metres above ground.  It is dropped and falls directly to the ground.  It hits the ground with a speed of $v$ m s^-1.

i) Find the decrease in gravitational potential energy of the brick between its starting point and the point when it hits the ground.

ii) Write an expression in terms of $v$ for the kinetic energy of the brick as it hits the ground.

iii) Use the conservation of mechanical energy principle to find the value of $v$. 

iv) Write an assumption you have made in part (iii).