Question

An eagle is observed to be flying in the sky towards its nest. If the eagle has mass of 42 kg and is flying with a speed of 26 m/s at an elevation (height) of 16 m above the ground, then calculate the total mechanical energy of the eagle. Be sure to express your answer with 2 decimal places and with the proper unit abbreviation.

Answer 1

The total mechanical energy of an eagle with a mass of 42 kg flying at 26 m/s at a height of 16 m is 20798.88 Joules. To get this, we sum its kinetic energy (14196 J) and gravitational potential energy (6602.88 J).

Step-by-step explanation:

To calculate the total mechanical energy of an eagle flying towards its nest, we need to consider both its kinetic energy and gravitational potential energy. The total mechanical energy is the sum of kinetic energy (K) and potential energy (U).

Step 1: Calculate the kinetic energy

The kinetic energy (K) of the eagle can be calculated using the formula:

K = (1/2) × mass × velocity^2

For the eagle with mass = 42 kg and velocity = 26 m/s:

K = (1/2) × 42 kg × (26 m/s)^2

K = 14196 J (rounded to two decimal places)

Step 2: Calculate the potential energy

The potential energy (U) of the eagle at a height of 16 m is:

U = mass × gravitational acceleration × height

Assuming standard gravitational acceleration of 9.81 m/s^2:

U = 42 kg × 9.81 m/s^2 × 16 m

U = 6602.88 J (rounded to two decimal places)

Step 3: Calculate the total mechanical energy

The total mechanical energy (E) is:

E = K + U

E = 14196 J + 6602.88 J

E = 20798.88 J (rounded to two decimal places)

Therefore, the total mechanical energy of the eagle flying at 26 m/s at an elevation of 16 m above the ground is 20798.88 J.