Final answer:
To find the final speed and time taken for a skier who skis along a slope, neglecting friction, starting from rest, we can use the equations of motion and conservation of energy. The final speed is approximately 20.6 m/s and the time taken is approximately 6.79 s. Despite the initial lack of advantage, a running start is still advantageous in competitive events to reach higher speeds and gain momentum before entering the slope.
Step-by-step explanation:
To find the final speed and time taken for a skier who skis 70.0 m along a 30° slope neglecting friction, we can use the equations of motion and conservation of energy. Starting from rest, the final speed can be found using the equation v = √(2gh), where g is the acceleration due to gravity and h is the change in height. The time taken can be found using the equation t = √(2h/g).
For a 30° slope, the change in height can be calculated as h = 70.0 m * sin(30°). Plugging in the values, the final speed is approximately 20.6 m/s and the time taken is approximately 6.79 s.
The answer might be surprising since one would expect a running start to provide an advantage. However, the gain in gravitational potential energy on even small hills is much greater compared to the initial kinetic energy. In very competitive events, a running start is still advantageous because it allows the skier to reach higher speeds and gain momentum before entering the slope.