If [tex]$196 \times 10^2$[/tex] J of energy is used to raise a 20 kg boy above the ground, how high would he be raised?

With 19600 J of energy, a 20 kg boy could be raised 980 meters above the ground using the gravitational potential energy formula, PE = mgh, and simplifying the acceleration due to gravity as 10 m/s².

Explanation:

To calculate how high a 20 kg boy would be raised with 196 * 10² J of energy, we use the formula for gravitational potential energy, PE = mgh, where PE represents potential energy in joules (J), m is the mass in kilograms (kg), g is the acceleration due to gravity (approximated as 10 m/s² for simplicity), and h is the height in meters (m) above the ground.

First, we express the energy in standard form:

196 * 10² = 19600 J

Given:
Mass, m = 20 kg.
Gravitational acceleration, g = 10 m/s².
Energy, PE = 19600 J.

To find the height, rearrange the formula to solve for h: h = PE / (mg).

Plug the values into the formula:

h = 19600 J / (20 kg * 10 m/s²) = 980 m.

Therefore, with 19600 J of energy, a 20 kg boy could be raised 980 meters above the ground.