Final answer:
To determine the distance traveled down the ramp by the snowboarder, we can use the work-energy theorem to equate the work done by gravity to the change in kinetic energy. By rearranging the equation and plugging in the given values, we can solve for the final velocity. Then, using the calculated final velocity, we can determine the distance traveled down the ramp by using the appropriate formula.
Step-by-step explanation:
To determine the distance traveled down the ramp by the snowboarder, we can use the work-energy theorem which states that the work done on an object is equal to the change in its kinetic energy. In this case, the work done by the force of gravity is equal to the change in the snowboarder's kinetic energy.
Given that the force of gravity does 2.6×10^4 J of work on the snowboarder, we can equate this to the change in kinetic energy:
2.6×10^4 J = 0.5 * mass * (final velocity^2 - initial velocity^2)
Since the snowboarder starts from rest, the initial velocity is 0. Plugging in the mass (68 kg) and solving for the final velocity:
2.6×10^4 J = 0.5 * 68 kg * (final velocity^2 - 0)
final velocity^2 = (2.6×10^4 J * 2) / 68 kg
final velocity = √((2.6×10^4 J * 2) / 68 kg)
The distance traveled down the ramp can then be calculated by using the equation: distance = (final velocity^2) / (2 * acceleration), where acceleration is the acceleration due to gravity multiplied by the sine of the angle of the incline:
distance = (final velocity^2) / (2 * (9.8 m/s^2) * sin(33°))
Substituting the value for the final velocity calculated earlier:
distance = (√((2.6×10^4 J * 2) / 68 kg)^2) / (2 * (9.8 m/s^2) * sin(33°))
Solving this equation will give us the distance traveled down the ramp by the snowboarder.