Question

Calculation of the velocity the marble had when it reaches the lowest point in your roller coaster. Ignore friction and air resistance.the mass of the marble is 18.5 grams. the height is 14 inches

Answer 1

Using the conservation of energy:

$\begin{gathered} E1=E2 \\ so: \\ K1+U1=K2+U2 \\ \frac{1}{2}mv1^2+mgh1=\frac{1}{2}mv2^2+mgh2 \\ Where: \\ h1=14 \\ h2=0 \\ v1=0 \\ \end{gathered}$

Therefore:

$\begin{gathered} mgh1=\frac{1}{2}mv2^2 \\ solve_{\text{ }}for_{\text{ }}v2: \\ v2=\sqrt{2gh1} \\ v2=\sqrt{2(9.8)(14)} \\ v2=\sqrt{274.4} \\ v2\approx16.565m/s \end{gathered}$

Answer:

16.565 m/s