Final answer:
The height of the ramp from which the skier departed can be determined by calculating the time of flight using the horizontal distance covered and initial velocity, and subsequently using this time to compute the vertical distance fallen under gravity.
Step-by-step explanation:
To calculate the height from which the skier left the ramp, we can use the principles of projectile motion. Since the skier lands 70 meters from the base after leaving the ramp horizontally at 25 m/s, we first determine the time of flight. The horizontal velocity is constant, as no acceleration occurs in the horizontal direction (assuming no air resistance). Therefore, time of flight can be calculated using the horizontal distance (d) and horizontal velocity (v):
Time, t = d/v = 70m / 25m/s = 2.8s
With time known, we can now calculate the height of the ramp using the vertical motion equations under constant acceleration due to gravity (g = 9.81 m/s2). We'll use the equation: s = ut + 0.5gt2, with the initial vertical velocity (u) being zero since the skier leaves the ramp horizontally.
Height, h = 0 + 0.5 × g × t2 = 0.5 × 9.81 m/s2 × (2.8s)2 ≈ 38.5 meters
Therefore, the end of the ramp is approximately 38.5 meters high from the ground.