Final answer:
To calculate the velocity needed for the basketball to have 160 J of kinetic energy, use the kinetic energy equation KE = (1/2)mv^2. The calculated velocity comes out to approximately 12.65 m/s, which does not match the given options, suggesting a possible error in the question.
Step-by-step explanation:
To determine how fast the 2.0 kg basketball must be thrown upward to achieve 160 J of energy, we use the formula for kinetic energy, KE = (1/2)mv2, where KE is kinetic energy, m is mass, and v is velocity. We need to find v such that KE equals 160 J. Solving for v gives us v = √(2KE/m).
Using the mass of the basketball, m = 2.0 kg, and the desired kinetic energy, KE = 160 J, we can calculate:
- v = √(2*160 J / 2.0 kg)
- v = √(160 J / 1.0 kg)
- v = √(160 J)
- v = 12.65 m/s
Since the options given are 10 m/s, 20 m/s, 30 m/s, and 40 m/s, none of the options exactly match the calculated velocity. The question may have an error or might be trick in nature.