Final answer:
A 0.4 kg ball dropped from 4.8 m will bounce up to a height of approximately 3.7 m after losing 4.3 J of energy to the environment upon impacting the ground.
Step-by-step explanation:
When you drop a 0.4 kg ball from a height of 4.8 m, the gravitational potential energy (PE) at the height before it drops is given by PE = mgh, where 'm' is the mass, 'g' is the acceleration due to gravity (9.8 m/s2), and 'h' is the height. So, the energy is PE = 0.4 kg * 9.8 m/s2 * 4.8 m = 18.816 J. After the impact, the ball loses 4.3 J to the environment. Therefore, the remaining energy is 18.816 J - 4.3 J = 14.516 J. This remaining energy is the gravitational potential energy at the maximum height it bounces back to (PEf).
PEf = mghf, where hf is the final height. To find the final height: hf = PEf / (mg) = 14.516 J / (0.4 kg * 9.8 m/s2) = 3.7 m. So, the ball will bounce up to a height of approximately 3.7 meters after losing energy to the environment upon impact.