A young child holds a ball over the edge of a balcony.the ball has 4kg and gravitational potential energy of 200J.the ball is then release.calculate the height of the balcony?

To calculate the height of the balcony, we can use the formula for gravitational potential energy:

PE = mgh

Where:
PE = gravitational potential energy (200 J)
m = mass of the ball (4 kg)
g = acceleration due to gravity (9.8 m/s^2)
h = height of the balcony

Rearranging the formula to solve for h:

h = PE / (mg)
h = 200 J / (4 kg * 9.8 m/s^2)
h = 5.1 meters

Therefore, the height of the balcony is 5.1 meters.

Given:
- Mass of the ball, m = 4 kg
- Gravitational potential energy, U = 200 J
- Acceleration due to gravity, g = 9.8 m/s²

Formula:
Gravitational potential energy (U) = m - g - h

where h is the height of the balcony.

Calculation:
Substituting the given values into the formula:

200 J = 4 kg - 9.8 m/s² - h
h = 200 J / (4 kg - 9.8 m/s²)
h = 5.1 meters

Therefore, the height of the balcony is 5.1 meters.