Final answer:
The ball would reach 31.9 meters with no energy lost. With only 25 meters reached, the work done against air resistance is 6.77 Joules. The average force of friction (air resistance) during the rise is 0.271 Newtons.
Step-by-step explanation:
To find the height the ball would reach if no energy is lost, we use the conservation of mechanical energy principle, whereby the initial kinetic energy (KE) is converted into gravitational potential energy (GPE) at the maximum height. The equation for this energy conversion is KE = GPE, which translates to ½ mv² = mgh, where m is the mass of the ball, v is the initial velocity, g is the acceleration due to gravity (9.81 m/s²), and h is the height. Solving for h, we get h = v² / (2g).
Plugging in the given values (m = 0.1 kg and v = 25 m/s), we calculate the height:
h = (25 m/s)² / (2 × 9.81 m/s²) = 31.9 m
Since the ball only rises to 25 m, we know that work done against air resistance (Wair) caused a loss of energy. The work done against air resistance is equal to the difference between the gravitational potential energy at the calculated height and the actual height, which is Wair = mghcalculated - mghactual.
Wair = 0.1 kg × 9.81 m/s² × (31.9 m - 25 m) = 6.77 J
We are asked to calculate the force of friction (air resistance). Considering that work is the product of force and distance, and knowing the work done and the distance, we can find the average force of friction. Therefore, F = Wair / d = 6.77 J / 25 m = 0.271 N.