#### Docks and Harbours

1

If h and h1 are the heights of a light house and the observer in a ship in metres above M S L then the horizontal distance from the ship to the light house in kilometres is

A. 3.86 (sqrt(h) + sqrt(h_1))
B. 3.86 (sqrt(h) - sqrt(h_1))
C. 3.86 (sqrt(h) xx sqrt(h_1))
D. 3.86 pi (sqrt(h) + sqrt(h_1))

2

The horizontal angles from the boat between A and B and B and C, the stations on the shore are respectively theta_1 and theta_2. The distances AB = L1 and BC = L2. For calculating the anglealpha_2 at C between the boat and station B is obtained by using the following formula: where (beta is horizontal angle between A and C at B).

A. (sin alpha_1)/(sin alpha_2) = (L_2 sin theta_1)/(L_1 sin theta_2) = K
B. alpha_t tan alpha_2 = 360^circ - ( theta_1 + theta_2 + beta) = phi
C. tan alpha_2 = (sin phi)/(K + cos phi)
D. all the above.

3

P and Q are two stations on the shore line at distance d. If the angle between Q and the boat O and P is a and the angle between P and Q at boat O is beta, the x and y. Coordinate along PQ and perpendicular to PQ from O are :

A.  x = (d tan beta)/(tan alpha + tan beta) ; Y = (d tan alpha tan beta)/(tan alpha + tan beta)
B.  x = (d tan beta)/(tan alpha - tan beta) ; Y = (d tan alpha tan beta)/(tan alpha - tan beta)
C.  x = (d tan alpha tan beta )/(tan alpha + tan beta) ; Y = (d tan beta )/(tan alpha + tan beta)
D. none of the above.

4
The wavelength is computed by Bertin's formula (where T is the period in seconds)

A. L = (T)/(2 pi) g
B. L = (T^2)/(2 pi) g
C. L = (2T)/( pi) g
D. L = (2T^2)/( pi) g

5

If F is the fetch, the straight line distance of open water available in kilometres, the height of the wave in metres is

A. 0.15 sqrt(F)
B. 0.20 sqrt(F)
C. 0.28 sqrt(F)
D. 0.34 sqrt(F)