Question

A body X, of mass 12Kg is placed 3metre above the ground, if another body Y, of mass 20kg moving with   velocity V, has a kinetic energy equal in value to the potential energy of X, calculate the magnitude of V.(g=10 m/s).

Answer 1

The potential energy of body X is:

$$E_p = m_xgh$$

where $m_x = 12kg$ is the mass of X, $h = 3m$ is its height, and $g = 10m/s^2$ is the gravitational acceleration.

The kinetic energy of Y is:

$$E_k = \dfrac{m_yv^2}{2}$$

where $m = 20kg$ is the mass of Y, and $v$ is its speed. SInce

$$E_p = E_k$$

obtain:

$$m_xgh = \dfrac{m_yv^2}{2}\\ v^2 = \dfrac{2ghm_x}{m_y}\\ v = \sqrt{\dfrac{2ghm_x}{m_y}}$$

Substituting the values, obtain:

$$v = \sqrt{\dfrac{2\cdot 10\cdot 3\cdot 12}{20}} = 6m/s$$

Answer. 6 m/s.