A 2.5 kg falcon soaring at a height of 500 meters has a certain potential energy. Now suppose the
falcon were carrying a 1.0 kg snake. What would the new height be if the total potential energy
were to remain the same?
PE=mgh
2.5g*500=(2.5+1.0)g*h
solve for h.
To determine the new height at which the falcon and snake combination would have the same potential energy as the falcon alone, we need to use the concept of conservation of energy.
The potential energy of an object at a certain height is given by the equation P.E. = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height.
In the given scenario, the falcon's potential energy is calculated as P.E. = (2.5 kg)(9.8 m/s^2)(500 m).
To keep the total potential energy the same, we need to equate the original falcon's potential energy with the combined potential energy of the falcon and snake.
So, (2.5 kg)(9.8 m/s^2)(500 m) = (2.5 kg + 1.0 kg)(9.8 m/s^2)(h).
Now, we can solve for h, the new height:
(2.5 * 9.8 * 500) = (3.5 * 9.8 * h)
12250 = 34.3h
h = 12250 / 34.3
h ≈ 357 meters
Therefore, the new height at which the falcon and snake combination would have the same potential energy as the falcon alone is approximately 357 meters.