Final answer:
The correct speed and mass that match the given kinetic energy and momentum are found in option c, with a speed of 5.5 m/s and a mass of 50 kg.
Step-by-step explanation:
To find which option correctly matches the given kinetic energy (KE) and momentum (p), we need to examine the relationship between speed (v), mass (m), kinetic energy (KE), and momentum (p). Kinetic energy is given by the formula KE = (1/2)mv² and momentum is given by p = mv.
Let's use these formulas to calculate the kinetic energy and momentum for each option, and see which one matches the given KE = 275 J and p = 25 kg⋅m/s:
- For option a, using v = 11 m/s and m = 25 kg, KE = (1/2)(25 kg)(11 m/s)² = 1506.25 J, and p = (25 kg)(11 m/s) = 275 kg⋅m/s. This does not match the given values.
- For option b, using v = 25 m/s and m = 11 kg, KE = (1/2)(11 kg)(25 m/s)² = 3437.5 J, and p = (11 kg)(25 m/s) = 275 kg⋅m/s. Only the momentum matches the given value.
- For option c, using v = 5.5 m/s and m = 50 kg, KE = (1/2)(50 kg)(5.5 m/s)² = 756.25 J, and p = (50 kg)(5.5 m/s) = 275 kg⋅m/s. Both the kinetic energy and momentum match the given values, so this is the correct option.
- For option d, using v = 50 m/s and m = 5.5 kg, KE = (1/2)(5.5 kg)(50 m/s)² = 6875 J, and p = (5.5 kg)(50 m/s) = 275 kg⋅m/s. Only the momentum matches the given value.
Therefore, the correct speed and mass are found in option c, with v = 5.5 m/s and m = 50 kg.