Final answer:
The potential energy of a 50 kg boy who approaches a hill on a skateboard and comes to a stop at Point 3 can be calculated using the conservation of energy. His initial kinetic energy, given by the velocity and mass, is converted to potential energy. However, upon calculation, the correct potential energy is 3,200 J, which is not one of the options provided.
Step-by-step explanation:
The question concerns the potential energy of a boy at Point 3 after he approaches a hill on a skateboard and comes to a stop. Assuming friction is negligible, we use the conservation of mechanical energy to find the potential energy. Initially, the boy has kinetic energy as he moves with a velocity of 8 m/s. When he stops at Point 3, all this kinetic energy has been converted into potential energy.
To calculate the potential energy (PE) at Point 3, we use the formula:
PE = m × g × h
where m is the mass of the boy, g is the acceleration due to gravity (9.81 m/s²), and h is the height that the boy has reached at Point 3. As the initial kinetic energy (KE) is totally converted into PE, we use the KE formula to find the height:
KE = ½ × m × v²
and since KE initial = PE at Point 3, we have:
½ × m × v² = m × g × h
Plugging in the values gives us:
½ × 50 kg × (8 m/s)² = 50 kg × 9.81 m/s² × h
Solving for h can be done by rearranging the formula and dividing by gravity and mass:
h = (½ × (8 m/s)²) / 9.81 m/s²
which gives us the height the boy has reached. Then we substitute this height into the potential energy formula to get the answer, which is 3,200 J, none of the proposed answers is correct.