Final answer:
The change in kinetic energy for objects with the same mass but different speeds illustrates the squared relationship between speed and kinetic energy. A 50 kg object moving at double the baseline speed has four times the kinetic energy, while one at half the speed has one-fourth the kinetic energy.
Step-by-step explanation:
To calculate the predicted change in kinetic energy (KE) for the given scenarios, we apply the kinetic energy formula KE = (1/2)mv², where m is the mass of the object and v is the velocity. It's essential to compare each state to the baseline scenario of a 50 kg ball traveling at 10 m/s. The baseline kinetic energy is (1/2)*50*10² = 2500 J (joules).
A 50 kg ball traveling at 20 m/s would have KE = (1/2)*50*20² = 10000 J. Compared to the baseline, this has four times more kinetic energy because kinetic energy is proportional to the square of the speed.
A 50 kg ball traveling at 5 m/s would have KE = (1/2)*50*5² = 625 J. This is one-fourth of the baseline kinetic energy, again showing the squared relationship with speed.
A 50 kg person falling at 10 m/s would have the same kinetic energy as the baseline, 2500 J, because both the mass and speed are the same as in the baseline scenario.