Problem 3-1

E = 25.75 cm  ANSWER.

Problem 3-2

E = 24.15 cm  ANSWER.

Problem 3-3

E = 11.54 cm  ANSWER.

Problem 3-4

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

At x = L = 250,000 m, elevation y = 28.65 m.

From Fig. 2-19, the area comprised between elevation 28.65 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:

A_t = ∫₀^250,000 y dx = ∫₀^250,000 100e^-0.000005x dx = 14,269,904

The area comprised between elevation 0 and elevation 28.65 m is:

A_b = 28.65 X 250,000 = 7,162,500 m². Therefore, the area A_p is:

A_p = A_t - A_b = 7,107,404 m².

S₂ = 2A_p/L² = 0.000227. ANSWER.