A object of mass m falls from a height h. Find its speed immediately prior to impact using conservation of mechanical energy. Neglect air resistance and assume constant gravitational field.

Question

A object of mass m falls from a height h. Find its speed immediately prior to impact using conservation of mechanical energy. Neglect air resistance and assume constant gravitational field.

Answer 1

Before it is dropped, the total energy of the mass is purely gravitational potential energy, given by mgh, where g is the gravitational acceleration at the surface of the Earth, 9.8 m*m/s and h is the height of the mass above the ground. As it falls and the height decreases, some of the potential energy is converted to kinetic energy, given by (1/2)mv*v, where v is the velocity of the mass. Just as the mass strikes the ground, its height is zero, so the total energy that was equal to mgh has been converted to purely kinetic energy, (1/2) mv*v.

Setting these expressions equal to one another and solving for v gives v = sqrt(2gh).