A cyclist does 300 J of work to climb a hill. If the cyclist's mass is 75 kg, wh

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Question: A cyclist does 300 J of work to climb a hill. If the cyclist\'s mass is 75 kg, what is the height of the hill? (2023)

Options:

Correct Answer: 0.5 m

Exam Year: 2023

Solution:

Potential Energy = mass × g × height; 300 J = 75 kg × 10 m/s² × height; height = 300 J / (75 kg × 10 m/s²) = 0.4 m

A cyclist does 300 J of work to climb a hill. If the cyclist's mass is 75 kg, what is the height of the hill? (2023)

A cyclist does 300 J of work to climb a hill. If the cyclist's mass is 75 kg, what is the height of the hill? (2023)

Step 1: Understand that the work done by the cyclist is equal to the potential energy gained when climbing the hill.
Step 2: Recall the formula for potential energy: Potential Energy = mass × g × height.
Step 3: Identify the values given in the problem: Work done (Potential Energy) = 300 J, mass = 75 kg, and g (acceleration due to gravity) = 10 m/s².
Step 4: Substitute the known values into the potential energy formula: 300 J = 75 kg × 10 m/s² × height.
Step 5: Rearrange the equation to solve for height: height = 300 J / (75 kg × 10 m/s²).
Step 6: Calculate the denominator: 75 kg × 10 m/s² = 750 kg·m/s².
Step 7: Divide 300 J by 750 kg·m/s² to find the height: height = 300 J / 750 kg·m/s² = 0.4 m.

Work and Energy – The relationship between work done, potential energy, and height in gravitational fields.
Gravitational Potential Energy – Understanding how mass, gravitational acceleration, and height relate to potential energy.