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------------------------------------------------ If [tex]196 \times 10^2 \, \text{J}[/tex] of energy were used to raise a 20 kg boy above the ground, how high would he be raised? (Given [tex]g = 9.8 \, \text{m/s}^2[/tex])

To find out the height the boy would be raised using the given amount of energy, we use the gravitational potential energy formula G.P.E. = mgh. By rearranging and solving for h with the provided values, we establish that the boy would be raised to a height of 100 meters above the ground.

Explanation:

The question is asking to calculate the height a boy would be raised given a certain amount of energy expended in lifting him against the force of gravity. The energy, also known as the gravitational potential energy (G.P.E.), is calculated using the formula:

G.P.E. = mgh

where:

m is the mass of the object being lifted (in kg)
g is the acceleration due to gravity (in m/s²)
h is the height above the ground (in m)

Given the energy value of 196×10² joules and the gravitational acceleration of 9.8 m/s², we can rearrange the formula to solve for the height h:

h = G.P.E. / (mg)

By plugging in the values we get:

h = (196×10² J) / (20 kg × 9.8 m/s²)

h = 19600 J / 196 N

h = 100 m

Therefore, the boy would be raised to a height of 100 meters above the ground.