Answer
See the detailed answer below.
Work Step by Step
We are given this equation;
$$\rm (1500\;kg)(9.8\;m/s^2)-11760\;N=(1500\;kg)\left(\dfrac{{\it v^2}}{200\;m}\right)$$
a) A 1500-kg mass of a roller coaster car on the top of its vertical circular path and the normal force exerted on it from the rails is 11760-N where the radius of this vertical circular path is 200 m. Find its speed at the top of its path.
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b) Solving the given formula for $v$;
$$v=\sqrt{[(1500\times 9.8)-11760]\dfrac{200}{1500}}$$
$$v=\color{red}{\bf 19.8}\;\rm m/s$$
