Final answer:
The kinetic energy of the 75 kg snowboarder before sliding up the frictionless rail to a height of 1.75 m while moving at 2.50 m/s was 1286.25 Joules, calculated using the conservation of energy principle.
Step-by-step explanation:
The kinetic energy the 75 kg snowboarder had before sliding up the rail to a height of 1.75 m while moving at a speed of 2.50 m/s. To solve this problem, we can use the principle of conservation of energy, assuming no frictional losses since the rail is described as frictionless. The snowboarder's potential energy at the top must equal his initial kinetic energy, as all kinetic energy will be converted into potential energy at the highest point.
Firstly, we calculate the potential energy (PE) at the height of 1.75 m using the formula PE = mgh, where:
- m = mass of the snowboarder (75 kg)
- g = acceleration due to gravity (9.8 m/s2)
- h = height (1.75 m)
PE = (75 kg)(9.8 m/s2)(1.75 m) = 1286.25 Joules
The kinetic energy (KE) the snowboarder had before sliding up the rail is equal to this potential energy, as no energy is lost to friction. Therefore, the initial kinetic energy of the snowboarder was 1286.25 Joules.