Exam-style question
Try this first
A roller coaster starts from rest at a height of 30 m. Calculate the speed at the bottom of the hill, assuming no energy is lost. Use g = 9.81 N/kg.
- A.24.3 m/s
- B.30 m/s
- C.15 m/s
- D.20 m/s
Model answer
What a good answer should say
- 24.3 m/s
Explanation
Why this works
Using conservation of energy, the gravitational potential energy at the top (Ep = mgh) converts to kinetic energy (Ek = 0.5mv^2) at the bottom. Setting them equal: mgh = 0.5mv^2.
The mass cancels out, giving gh = 0.5v^2. Substituting h = 30 m and g = 9.81 N/kg: 9.81 x 30 = 0.5v^2.
This simplifies to 294.3 = 0.5v^2, leading to v^2 = 588.6, and v = √588.6 ≈ 24.3 m/s. Thus, the speed at the bottom is approximately 24.3 m/s.
Common mistake
No common mistake is linked to this question yet.