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))`

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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 angle`alpha_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.

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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.

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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`

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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)`

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