Question

la Assume the roller coaster experiences no friction. What would be the speed of the rollercoaster at point F? Defend your answer in 1-2 sentences. (2 points)Speed at Point Fin mis:The reason is:

Answer 1

The conservation of mechanical energy states that:

$K_i+U_i=K_f+U_f$

Where K is the kinetic energy and U is the potential energy. We know that the potential energy is given as:

$K=\frac{1}{2}mv^2$

and the potential energy is given as:

$U=mgh$

We know that in point A the velocity is zero, then the kinetic energy in that point is zero. We also know the heights in point A and F then we can plug the vaus we know in the conservation of energy and solve for the velocity in point F:

$\begin{gathered} mgh_A=\frac{1}{2}mv^2+mgh_F \\ gh_A=\frac{1}{2}v^2+gh_F \\ gh_A-gh_F=\frac{1}{2}v^2 \\ v^2=2(gh_A-gh_F) \\ v=\sqrt[]{2g(h_A-h_F)} \\ v=\sqrt[]{2(9.8)(30-15)} \\ v=\sqrt[]{294} \\ v=17.15 \end{gathered}$

Therefore the velocity in point F is 17.15 m/s