To determine the height from which the basketball falls, we can use the principle of conservation of energy. The potential energy the basketball possesses at the initial height is converted into kinetic energy when it reaches the ground. We can equate the initial potential energy to the final kinetic energy to solve for the height.
The potential energy (PE) of an object at a certain height is given by the formula:
PE = m * g * h
Where:
- m is the mass of the basketball (2 kg)
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
- h is the height from which the basketball falls
The kinetic energy (KE) of an object with a certain velocity is given by the formula:
KE = (1/2) * m * v^2
Where:
- v is the velocity of the basketball when it hits the ground (7 m/s)
Since the potential energy is converted entirely into kinetic energy at the moment of impact, we can equate the two equations:
PE = KE
m * g * h = (1/2) * m * v^2
Simplifying the equation by canceling out the mass:
g * h = (1/2) * v^2
Now we can substitute the known values and solve for h:
(9.8 m/s^2) * h = (1/2) * (7 m/s)^2
9.8 * h = 0.5 * 49
9.8 * h = 24.5
h = 24.5 / 9.8
h ≈ 2.5 meters
Therefore, the basketball was dropped from a height of approximately 2.5 meters.