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‘Skysails’ is that genre of engineering ...

‘Skysails’ is that genre of engineering science that uses extensive utilization of wind energy to move a vessel in the sea water. The ‘Skysails’ technology allows the towing kite to gain a height of anything between 100 metres – 300 metres.The sailing kite is made in such a way that it can be raised to its proper elevation and then brought back with the help of a ‘telescopic mast’ that enables the kite to be raised properly and effectively.
Based on the following figure related to sky sailing, answer the questions
ltimg src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/MATH_041_X_SQP_E02_005_Q01.png" width="80%"gt
(i) In the given figure, if `sin theta = cos (3theta - 30^(@)),` where `theta` and `3theta- 30^(@)` are acuts angle, then find the value of `theta`.
(ii) What should be the length of the rope of the kite sail in order to pull the ship at the angle `theta` (calculated above) and be at a vertical height of 200 m?

Text Solution

Verified by Experts

(i) `cos (90^(@) -theta) = cos(3theta - 30^(@))`
`rArr 90^(@) - theta = 3theta - 30^(@) rArr theta= 30^(@)`
(ii) `(AB)/(AC) = sin 30^(@)`
`therefore"Lenght of rope" = AC = 400m`
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