.Sure, here are the calculations to find the length of the incline (l):
Given:
Initial speed (v₀) = 5.0 m/s
Final speed (v) = 17 m/s
Incline angle (θ) = 13 degrees
Calculate acceleration (a):
a = (v² - v₀²) / (2 * g * sinθ),
a = (17² - 5.0²) / (2 * 9.8 * sin(13°)),
a ≈ 3.455 m/s².
Calculate time (t):
t = (v - v₀) / a,
t = (17 - 5.0) / 3.455,
t ≈ 3.47 s.
Calculate length of incline (l):
l = v₀ * t + (1/2) * a * t²,
l = 5.0 * 3.47 + (1/2) * 3.455 * (3.47)²,
l ≈ 309.1 meters.