What is the maximum height achieved if a 0.800 kg mass is thrown straight upward with an initial...

Question:

What is the maximum height achieved if a 0.800 kg mass is thrown straight upward with an initial speed of {eq}40.0 \ m \cdot s^{-1} {/eq}?

Conservation and Conversion of Energy

The law of conservation of energy states that energy can neither be created nor destroyed, but only converted from one form to another. There are various types of energy in science: kinetic energy, which a body has by virtue of its motion, potential energy, due to its position in a gravitational field, thermal energy, due to microscopic vibrations of the atoms about a mean position, etc.

The kinetic energy of the mass at the point of throw is maximum, and its potential energy is zero, assuming the datum is the position of departure of the mass.

Then, as the mass moves upwards, its kinetic energy is gradually converted to potential energy, causing it to slow down. At its maximum height, it is momentarily at rest, implying that its kinetic energy is zero and its potential energy is maximum.

The conclusion from this explanation is that the kinetic energy at the point of throw is all converted into potential energy at the maximum height. Now, we may express this mathematically as:

{eq}\displaystyle \frac{1}{2}mv^2 = mgh {/eq}.

The mass ({eq}m {/eq}) cancels out, leaving us with:

{eq}\displaystyle \begin{align} h &= \frac{v^2}{2g} \\ &= \frac{40^2 \ m^2/s^2}{2 \times 9.81 m/s^2}\\ &= 81.55 \ m \end{align} {/eq}