question 25 of 27\na roller coaster has a mass of 450 kg. it sits at the top of a hill with height 49 m. if…

Explanation:

Step1: Apply conservation of energy

At the top, the roller - coaster has only potential energy $U = mgh$. At the bottom, it has only kinetic energy $K=\frac{1}{2}mv^{2}$. Since energy is conserved ($U = K$), we have $mgh=\frac{1}{2}mv^{2}$.

Step2: Solve for velocity $v$

First, cancel out the mass $m$ from both sides of the equation $mgh=\frac{1}{2}mv^{2}$. We get $gh=\frac{1}{2}v^{2}$. Then, solve for $v$: $v = \sqrt{2gh}$. Given $g = 9.8\ m/s^{2}$ and $h = 49\ m$, we substitute these values into the formula. $v=\sqrt{2\times9.8\times49}=\sqrt{960.4}\approx 31.0\ m/s$.

Answer:

D. 31.0 m/s