Review: Physics student Eileen Dover has gone to the state fair and is about to perform an experiment on a roller coaster. She will sit on a metric bathroom scale which gives her weight in Newtons. As she sits in the roller coaster car waiting for the ride to start, the scale reads $392N.$

a$)$ At the very top of the second hill, she looks at the bathroom scale and it reads only $8N.$ What is her downward acceleration? Include a free body diagram. Let $g=9\mathrm{.}8\frac{m}{s^2}$

b$)$ At the very bottom of the next valley she looks around and realizes that though her horizontal motion is fairly constant, she is accelerating upward at $49\frac{m}{s^2}.$ What does the bathroom scale read now? Include a free body diagram. Let $g=9\mathrm{.}8\frac{m}{s^2}$