Answer: the ball is moving at a speed of approximately 9.90 m/s once it has fallen 5 meters, assuming there is no air resistance.
Step-by-step explanation:
To solve this problem, we can use the conservation of energy principle, which states that the total energy of a system remains constant, although it may be converted from one form to another. In this case, the initial potential energy of the ball (due to its position above the ground) is converted to kinetic energy (due to its motion) as the ball falls. At the point where the ball has fallen 5 meters, we can use the following equation to find the speed of the ball:
PE(initial) = KE(final)
mgh = 1/2mv^2
Here, m is the mass of the ball (8 kg), g is the acceleration due to gravity (9.81 m/s^2), h is the distance fallen (5 m), and v is the final velocity of the ball.
Solving for v, we get:
v = √(2gh)
v = √(2 x 9.81 m/s^2 x 5 m)
v = √(98.1 m^2/s^2)
v = 9.90 m/s (rounded to two decimal places)
Therefore, the ball is moving at a speed of approximately 9.90 m/s once it has fallen 5 meters, assuming there is no air resistance.