# To enter the main pool at an amusement part, a swimmer uses a water slide which has a vertical...

## Question:

To enter the main pool at an amusement part, a swimmer uses a water slide which has a vertical height of 2.65 m. Find her speed at the bottom of the slide if she starts with an initial speed of 0.950 m/s.

## Energy conservation:

The principle of energy conservation states that the energy of a system remains conserved if there is no external force present on the system.

The water slide is nearly frictionless so there is no frictional force on the slide. Then the total mechanical energy at the highest point of the slide should be equal to the total mechanical energy at the lowest point.

Given:

The vertical height of the slide is, {eq}h = 2.65\ m {/eq}

The initial speed is {eq}u = 0.950 m/s. {/eq}

Let the velocity at the bottom be v.

By the conservation of energy,

\begin{align} 0.5\ m\ u^2 + m\ g\ h &= 0.5\ m\ v^2\\ 0.5\times 0.950^2 + 9.81\times 2.65 &= 0.5\ v^2\\ 0.451 + 25.99 &= 0.5\ v^2\\ 52.88 &= v^2\\ \implies v &= 7.27\ m/s\\ \end{align} 