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A cyclist is moving up a hill and gains 3000 J of potential energy. If the mass

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Question: A cyclist is moving up a hill and gains 3000 J of potential energy. If the mass of the cyclist and the bicycle is 75 kg, what is the height of the hill? (g = 9.8 m/s²)

Options:

  1. 4.08 m
  2. 3.06 m
  3. 2.04 m
  4. 1.5 m

Correct Answer: 4.08 m

Solution: 

Height (h) = PE / (mg) = 3000 J / (75 kg * 9.8 m/s²) = 4.08 m.

A cyclist is moving up a hill and gains 3000 J of potential energy. If the mass

Practice Questions

Q1
A cyclist is moving up a hill and gains 3000 J of potential energy. If the mass of the cyclist and the bicycle is 75 kg, what is the height of the hill? (g = 9.8 m/s²)
  1. 4.08 m
  2. 3.06 m
  3. 2.04 m
  4. 1.5 m

Questions & Step-by-Step Solutions

A cyclist is moving up a hill and gains 3000 J of potential energy. If the mass of the cyclist and the bicycle is 75 kg, what is the height of the hill? (g = 9.8 m/s²)
  • Step 1: Understand that potential energy (PE) is given by the formula PE = mgh, where m is mass, g is the acceleration due to gravity, and h is height.
  • Step 2: Identify the values given in the problem: PE = 3000 J, m = 75 kg, and g = 9.8 m/s².
  • Step 3: Rearrange the formula to solve for height (h): h = PE / (mg).
  • Step 4: Calculate the product of mass (m) and gravity (g): 75 kg * 9.8 m/s² = 735 kg·m/s².
  • Step 5: Divide the potential energy (PE) by the product from Step 4: h = 3000 J / 735 kg·m/s².
  • Step 6: Perform the division: h = 4.08 m.
  • Potential Energy – The energy stored in an object due to its height above the ground, calculated as PE = mgh.
  • Gravitational Force – The force acting on an object due to gravity, which is the product of mass and gravitational acceleration (mg).
  • Height Calculation – Determining the height of an object based on the potential energy gained and the mass of the object.
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