Answer :
The skier, who has a mass of 103 kg and does 3,675 J of work in moving uphill and whose speed is 3.4 m/s at the top, ascended to a height of approximately 31.77 meters.
In physics , we use the principle of conservation of energy. This principle states that the total energy of an isolated system remains constant.
Here, the skier's energy consists of potential energy
(PE = m*g*h, where m is mass, g is acceleration due to gravity and h is height) and kinetic energy
(KE = 0.5*m*v2).
First, we know that the total energy is supplied by the work done, which is 3,675 J.
Also, we know the
mass (m = 103 kg),
gravity (g = 9.8 m/s2), and
speed (v = 3.4 m/s).
The kinetic energy (KE) would be 0.5 * 103 kg * (3.4 m/s)2 = 595.46 J. This value is subtracted from the work done to get the potential energy.
The potential energy is then used to find the height:
PE = m*g*h, rearranges for height as
h = PE / (m*g).
So, h = (3675 J - 595.46 J) / (103 kg * 9.8 m/s2)
= 31.77 m.
The skier moved uphill to a height of approximately 31.77 meters.
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