Feb 20, 2017

$26.4 m {s}^{-} 1$ rounded to one decimal place.

#### Explanation:

At the top Potential energy of roller coaster car$= m g h$
Kinetic energy at any instant of time $= \frac{1}{2} m {v}^{2}$

At the bottom all potential energy gets converted into Kinetic energy of the roller coaster car.

Ignoring friction and using law of Conservation of energy we get
$m g h = \frac{1}{2} m {v}_{\max}^{2}$
$\implies {v}_{\max}^{2} = 2 g h$
$\implies {v}_{\max} = \sqrt{2 g h}$

Inserting values we get
${v}_{\max} = \sqrt{2 \times 9.81 \times 35.4}$
$\implies {v}_{\max} = 26.4 m {s}^{-} 1$ rounded to one decimal place.