Final answer:
To calculate the gravitational potential energy and kinetic energy of a 2 kg ball, formulas PE = mgh and KE = 1/2 mv² are used. The kinetic energy at 15 m/s is 225 J. Without the height, the gravitational potential energy cannot be determined, but the total mechanical energy is the sum of both energies.
Step-by-step explanation:
When calculating the gravitational potential energy (PE) of an object, the formula PE = mgh is used, where m is the mass of the object, g is the acceleration due to gravity, and h is the height above the reference point. For kinetic energy (KE), the formula KE = 1/2 mv² is used, with v representing the velocity of the object.
For a 2 kg ball traveling at 15 m/s at position 1:
- The kinetic energy is KE = 1/2 (2 kg)(15 m/s)² = 225 J.
- If the ball is at a height h, the gravitational potential energy can be calculated assuming Earth's gravity is approximately 9.81 m/s². However, without knowing the height, we cannot calculate the exact potential energy.
- The total mechanical energy (TME) is the sum of kinetic and potential energies, TME = KE + PE.
Assuming no energy losses and that the gravitational potential energy is set to zero at the launch position:
- The gravitational potential energy at the highest point will be equal to the kinetic energy initially due to conservation of energy.
- The velocity at any position can be found by using the conservation of mechanical energy principle.