Answer:
a) 14 m/s
Explanation:
The net force at the top of the roller coaster is the apparent weight of the passenger, so by the second law of newton
[tex]\begin{gathered} F_{\text{net}}=ma_c \\ mg=ma_c \end{gathered}[/tex]Where m is the mass of the passenger, g is the gravity and ac is the centripetal acceleration. The centripetal acceleration is also equal to v²/r where v is the speed and r is the radius of the roller coaster. Then, we can write the equation as
[tex]mg=m(\frac{v^2}{r})[/tex]Solving for v, we get:
[tex]\begin{gathered} \frac{mg}{m}=\frac{v^2}{r}^{}_{} \\ g=\frac{v^2_{}}{r} \\ gr=v^2^{}_{} \\ v=\sqrt[]{gr} \end{gathered}[/tex]So, replacing g = 9.8 m/s² and r = 20.0 m because the radius is half the diameter, we get:
[tex]\begin{gathered} v=\sqrt[]{(9.8)(20)} \\ v=14\text{ m/s} \end{gathered}[/tex]Therefore, the car's speed at the top is 14 m/s