Question

a: calculate the total mechanical energy of the person on the bridge relative to waterb:calculate the total mechanical energy of the person as he enters relative to the waterc: calculate the speed of the person as he enters the water using energy equations onlyd:calculate the speed of the person when he is 10m above the water using energy equations onlye:describe the energy conversion taking place as the person moves from the bridge to the river below the bridge.

Answer 1

a.

The mechanical energy is given by the sum of potential and kinetic energies:

`ME=PE+KE`

When the person is on the bridge, the kinetic energy is zero (the person it at rest) and there is potential energy in relation to the water, which is given by:

`\begin{gathered} ME=mgh+(mv^2)/(2)\\ \\ ME=70\cdot9.8\cdot30+0\\ \\ ME=20580\text{ J} \end{gathered}`

b.

When the person enters the water, all the potential energy he/she had was converted into kinetic energy, but if we have no energy loss, the mechanical energy is still the same, therefore the total mechanical energy is 20,580 J.

c.

Since the height relative to the water is zero, let's use all the mechanical energy as kinetic energy:

`\begin{gathered} ME=0+(mv^2)/(2)\\ \\ 20580=70\cdot(v^2)/(2)\\ \\ v^2=(20580)/(35)\\ \\ v^2=588\\ \\ v=24.25\text{ m/s} \end{gathered}`

d.

In this case, we have both potential and kinetic energies:

`\begin{gathered} ME=mgh+(mv^2)/(2)\\ \\ 20580=70\cdot9.8\cdot10+(70v^2)/(2)\\ \\ 20580=6860+35v^2\\ \\ 35v^2=13720\\ \\ v^2=392\\ \\ v=19.8\text{ m/s} \end{gathered}`

e.

As the height of the person relative to the water decreases, he/she potential gravitational energy will be converted into kinetic energy (the person's velocity will increase as the height decreases).