# If the coaster is going to make it to point C it needs to start with some initial velocity. If...

## Question:

If the coaster is going to make it point C it needs to start with some initial velocity. If point C is 21 meters high and the coaster starts at a height of 20 meters, What would its initial velocity need to be if no energy is lost to friction?

## Application of Conservation of Energy :

We will solve this problem by using the conservation of energy. Since there is no loss in energy due to the friction. The total energy of the coaster will be conserved.

## Answer and Explanation:

Let the coaster needs to start with minimum speed {eq}v {/eq} so that it can reach {eq}21\ \rm m {/eq} and it has mass {eq}m {/eq}

Hence initial total energy {eq}=\dfrac12mv^2+mgh=\dfrac12mv^2+20mg {/eq}

Since here we are considering minimum speed, therefore, finally, the coaster will have no velocity. It would just barely reach {eq}21\ \rm m {/eq}

Hence final total energy {eq}=\dfrac12mv^2+mgh=0+21mg {/eq}

Now using conservation of energy we get,

\begin{align} &\dfrac12mv^2+20mg=21mg\\[.3 cm] &\dfrac12mv^2=mg\\[.3 cm] &v^2=2g\\[.3 cm] &v=\sqrt{2g}\\[.3 cm] &v=\sqrt{2(9.8\ \rm m/s^2)}\\[.3 cm] &v\approx 4.43\ \rm m/s \end{align}

Hence the coaster need to start with at least velocity of 4.43 m/s.

Energy Conservation and Energy Efficiency: Examples and Differences

from Geography 101: Human & Cultural Geography

Chapter 13 / Lesson 9
108K