Answer: 81.619 kJ
Explanation:
Given
Mass of roller coaster is [tex]m=230\ kg[/tex]
It reaches the steepest hill with speed of [tex]u=6.2\ km/h\ or \ 1.72\ m/s[/tex]
Hill to bottom is 51 m long with inclination of [tex]45^{\circ}[/tex]
Height of the hill is [tex]h=51\sin 45^{\circ}=36.06\ m[/tex]
Conserving energy to get kinetic energy at bottom
Energy at top=Energy at bottom
[tex]\Rightarrow K_t+U_t=K_b+U_b\\\Rightarrow \dfrac{1}{2}mu^2+mgh=K_b+0\\\\\Rightarrow K_b=0.5\times 230\times 1.72^2+230\times 9.8\times 36.06\\\Rightarrow K_b=340.216+81,279.24\\\Rightarrow K_b=81,619.456\ J\\\Rightarrow K_b=81.619\ kJ[/tex]
