Final answer:
To find the final speed of the skateboarder after traveling up the ramp, we can use the principle of conservation of energy.
Step-by-step explanation:
The skateboarder starts up a 3.0 m long ramp with an initial speed of 42 m/s. To find the final speed after traveling up the ramp, we can use the principle of conservation of energy. Since we know the initial speed and the height of the ramp, we can calculate the final speed using the equation:
vf^2 = vi^2 + 2ad
where vf is the final speed, vi is the initial speed, a is the acceleration (which can be calculated using the incline angle of the ramp), and d is the distance traveled up the ramp.