a roller coaster has a mass of 425 kg. it sits at the top of a hill with height 66 m. if it drops from this…
a roller coaster has a mass of 425 kg. it sits at the top of a hill with height 66 m. if it drops from this hill, how fast is it going when it reaches the bottom? (assume there is no air resistance or friction.)\na. 36.0 m/s\nb. 56.8 m/s\nc. 12.5 m/s\nd. 91.3 m/s
Answer
Explanation:
Step1: Apply conservation of energy
Initial potential energy $U = mgh$ and final kinetic energy $K=\frac{1}{2}mv^{2}$. Since there is no air - resistance or friction, $U = K$. So $mgh=\frac{1}{2}mv^{2}$.
Step2: Solve for velocity $v$
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 $v=\sqrt{2gh}$. Given $g = 9.8\ m/s^{2}$ and $h = 66\ m$, substitute these values: $v=\sqrt{2\times9.8\times66}$.
Step3: Calculate the value of $v$
$v=\sqrt{1293.6}\approx36.0\ m/s$.
Answer:
A. 36.0 m/s