High School

If 196 x 100 J of energy were used to raise a 20 kg boy above the ground, how high would he go?

(Given [tex]g = 9.8 \, \text{m/s}^2[/tex])

Answer :

Final answer:

Using the gravitational potential energy formula, the 20 kg boy would rise approximately 1,000 meters above the ground when 196,000 J of energy is used to lift him.

Explanation:

The student's question involves calculating the height to which a 20 kg boy would rise given 196,000 J of energy is used to lift him from the ground. This scenario is a classic example of conservation of energy, where the energy used is converted into gravitational potential energy. The formula to calculate height (h) is derived from the gravitational potential energy equation:

Energy = mgh

Where:

  • m = mass in kilograms
  • g = acceleration due to gravity, which is 9.8 m/s² on Earth
  • h = height in meters

Rearranging the formula to solve for height, we get:

h = Energy / (mg)

Plugging in the values given:

h = 196,000 J / (20 kg * 9.8 m/s²)

h = 196,000 J / (196 kg*m/s²)

h = 1,000 m

Therefore, the boy would rise approximately 1,000 meters above the ground.

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