Final answer:
The speed of a 56 kg person who jumps from a 10 m platform and is 2.21 m above the water is calculated using the conservation of energy. The potential energy at the starting height is converted into kinetic energy as the person falls. The correct speed when the person is 2.21 m above the water is 7.71 m/s.
Step-by-step explanation:
The student asks about the speed of a 56 kg person when they are 2.21 m above the water after jumping from a 10 m platform. To solve this, we can use the principle of conservation of energy where potential energy at the top is converted to kinetic energy as the person falls. The potential energy (PE) at the top is given by PE = mgh, where m is mass, g is the acceleration due to gravity (9.8 m/s2), and h is the height. The kinetic energy (KE) at 2.21 m above the water is given by KE = 0.5mv2, where v is the velocity we want to find.
In the absence of air resistance, the potential energy lost equals kinetic energy gained, so mgh1 = 0.5mv2 + mgh2, where h1 is the initial height (10 m) and h2 is the final height (2.21 m). After canceling mass m from both sides and plugging in the values, we solve for v which represents the velocity of the person at 2.21 m above water.
After calculations, we find that the correct answer is (a) 7.71 m/s, therefore the speed of the person when they are 2.21 m above the water after jumping from a 10 m platform is 7.71 m/s.