Problem 3-2

E = 18.88 cm  ANSWER.

Problem 3-3

E = 12.23 cm  ANSWER.

Problem 3-4

At x = 0 km: elevation y = 100 m.

At x = L = 300,000 m: elevation y = 22.313 m.

From Fig. 2-19, the area comprised between elevation y = 22.313 and the longitudinal profile is:   A_p = YL/2.

Therefore, the S₂ slope is:   S₂ = Y/L = 2A_p/L².

The total area, A_t, below the longitudinal profile is obtained by integration between the limits of 0 and 300,000:

A_t = ∫₀^300,000 y dx = ∫₀^300,000 [100e^-0.000005x ] dx = 15,537,396.8

The area comprised between elevation 0 and elevation 22.313 m is:

A_b = 22.313 • 300,000 = 6,693,900 m².

Therefore, the area A_p is:

A_p = A_t - A_b = 8,843,496.8 m².

S₂ = 2A_p/L² = 0.0001965   ANSWER.