A ship of length $l = 150 m$ moving with velocity $υ_{s} = 36 k m / h$ on the sea suddenly discovered a sinking boat straight ahead. A rescue boat has been lowered from the mid of the ship, which went to the sinking boat with speed $v_{b} = 72 k m / h .$ When the rescue boat overtakes the leading edge of the ship, the sinking boat was $x_{0} = 3.0 k m$ away. The rescue boat reaches the sinking boat, spends $t_{0} = 1.0$ min there to take the people on board and then returns with the same speed. Determine time taken in seconds in the whole rescue operation from the moment the rescue boat was lowered to the moment the rescue boat returned to the mid of the ship from where it was lowered.

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answer is 250.

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Detailed Solution

$\frac{l}{2 (υ_{b} - υ_{s})} + \frac{1}{(υ_{b} + υ_{s})} (\frac{l}{2} + 2 x_{0} + υ_{b} t_{0}) = 250 s$

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