1) Total energy at the initial point is the sum of potential and kinetic energy.
PE_initial = mgh = 100 kg * 9.81 m/s² * 20 m = 19620 J
KE_initial = ½mv₀² = ½ * 100 kg * (2 m/s)² = 200 J
Total Energy = PE_initial + KE_initial = 19620 J + 200 J = 19820 J
2) Potential energy at point A is calculated using the same height h as the first hill.
PE_A = mgh = 100 kg * 9.81 m/s² * 20 m = 19620 J
3) Using conservation of energy, total energy at point B equals total energy at the initial point.
Total Energy = PE_B + KE_B
PE_B = mg(h/2) = 100 kg * 9.81 m/s² * (20 m / 2) = 9810 J
KE_B = Total Energy - PE_B = 19820 J - 9810 J = 10010 J
4) Point C is at ground level, so its height is 0.
PE_C = mg * 0 = 0 J
5) Using conservation of energy, total energy at point C equals total energy at the initial point.
Total Energy = PE_C + KE_C
KE_C = Total Energy - PE_C = 19820 J - 0 J = 19820 J
6) Use the kinetic energy at point C to find the velocity.
KE_C = ½mv_C²
19820 J = ½ * 100 kg * v_C²
v_C² = (19820 J * 2) / 100 kg = 396.4 m²/s²
v_C = √396.4 ≈ 19.91 m/s
Parent Tip: Review the logic above to help your child master the concept of roller coaster physics worksheet.
