Final answer:
The initial potential energy of the bear, calculated using energy conservation principles and the formula for gravitational potential energy, is 392.682 Joules.
Step-by-step explanation:
To determine the initial potential energy of the bear, we can use the concept of gravitational potential energy given by the formula U = mgh, where U is the potential energy, m is the mass of the bear, g is the acceleration due to gravity (9.81 m/s2), and h is the height from which the bear slides. Here, we are not provided with the height h directly. However, we can determine it using the principles of energy conservation because the bear starts from rest and possesses only potential energy at the start which is then converted into kinetic energy at the bottom.
The kinetic energy (KE) of the bear at the bottom is given by KE = 1/2 mv2, where v is the speed of the bear at the bottom. By setting the initial potential energy of the bear equal to its kinetic energy at the bottom (assuming no energy is lost due to friction), we can solve for h:
U = KE
mgh = 1/2 mv2
h = (v2) / (2g)
h = (5.56 m/s)2 / (2 × 9.81 m/s2)
h = 1.58 m
Now with the height determined, we can find the initial potential energy:
U = mgh
U = 25.3 kg × 9.81 m/s2 × 1.58 m
U = 392.682 J
The initial potential energy of the bear is 392.682 Joules.