Final answer:
The kinetic energy at point B (Kb) minus the kinetic energy at point A (Ka) is determined by first calculating the potential energy at point A and assuming it converts to kinetic energy at point B due to the conservation of energy, resulting in Kb - Ka = 15.68 J - unknown initial KE at A.
Step-by-step explanation:
To determine the value of the kinetic energy of the ball at point B minus the kinetic energy of the ball at point A (Kb - Ka), we need to apply the principles of energy conservation.
Calculate the potential energy at point A:
The potential energy (PE) at point A can be calculated using the formula PE = mgh, where m is mass, g is the acceleration due to gravity (9.8 m/s²), and h is the height. Since the ball is at a height of 30 m plus the additional 10 m (the maximum height above the building), the total height (h) is 40 m.
PE at A = (0.04 kg) × (9.8 m/s²) × (40 m) = 15.68 J
Calculate the kinetic energy at point B:
At point B, just before striking the ground, all the potential energy at the highest point (point A) would have been converted to kinetic energy (KE) due to energy conservation in the absence of air resistance. The kinetic energy at point B can be calculated using the formula KE = 0.5 × m × v², where v is the velocity of the ball at point B, which can be found using the principle that the potential energy at point A equals the kinetic energy at point B (PE at A = KE at B).
15.68 J = 0.5 × (0.04 kg) × v²
v² = (15.68 J) / (0.02 kg) = 784 m²/s²
v = √784 m²/s² = 28 m/s
KE at B = 0.5 × (0.04 kg) × (28 m/s)² = 15.68 J
Calculate Kb - Ka:
Since at point A the ball is thrown, it already has some kinetic energy in addition to its potential energy, but without the initial velocity we can't calculate the exact kinetic energy at A. However, for the difference Kb - Ka, we can say that the kinetic energy at B is purely from the conversion of its potential energy at A.
So, Kb - Ka = KE at B - KE at A