Final answer:
The total mechanical energy of a robin flying at 8.00 m/s with a mass of 0.300 kg and at a height of 35.0 m above the ground is 113.205 J.
Step-by-step explanation:
The total mechanical energy of the robin 35.0 meters above the ground can be calculated by summing its potential and kinetic energies. The potential energy (PE) due to gravity is given by the formula PE = mgh, where m is mass, g is the acceleration due to gravity (approximately 9.81 m/s2), and h is the height above the ground. The kinetic energy (KE) of the robin due to its horizontal motion is given by the formula KE = (1/2)mv2, where m is mass and v is velocity.
Using the given values, PE = (0.300 kg)(9.81 m/s2)(35.0 m) and KE = (1/2)(0.300 kg)(8.00 m/s)2.
Therefore, the total mechanical energy (TME) of the robin is the sum of its PE and KE:
- PE = (0.300 kg)(9.81 m/s2)(35.0 m) = 103.605 J
- KE = (1/2)(0.300 kg)(8.00 m/s)2 = 9.6 J
- TME = PE + KE = 103.605 J + 9.6 J = 113.205 J