Answer
a) Top speed of the roller coaster, v = 15 m/s
Maximum height reached by the roller coaster, h = ?
Using conservation of energy
[tex]\dfrac{1}{2}mv^2 = m gh[/tex]
[tex]h = \dfrac{v^2}{2g}[/tex]
[tex]h = \dfrac{15^2}{2\times 9.81}[/tex]
[tex]h= 11.47\ m[/tex]
b) Maximum height, H = 80 m
Top speed of the roller coaster, v = ?
Using conservation of energy
[tex]\dfrac{1}{2}mv^2 = m gh[/tex]
[tex]v = \sqrt{2gh}[/tex]
[tex]v = \sqrt{2\times 9.81\times 80}[/tex]
[tex]v = 39.62\ m/s[/tex]
