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)
Practice Questions
1 question
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)
4.08 m
3.06 m
2.04 m
1.5 m
Height (h) = PE / (mg) = 3000 J / (75 kg * 9.8 m/s²) = 4.08 m.
Questions & Step-by-step Solutions
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Q
Q: 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)
Solution: Height (h) = PE / (mg) = 3000 J / (75 kg * 9.8 m/s²) = 4.08 m.
Steps: 6
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.
