JOMO 6, Short 5

Geometry Level 3

A man was standing on the top of a \(300 \text{m}\) tall tower on coast of Arabic sea. He saw a ship in the sea which was coming towards the coast with a uniform velocity. The angle of depression with which he had to see the ship was \(30^{\circ}\). After 40 seconds that angle of depression was seen to be \(45^{\circ}\). Let the speed of the ship be \(x\) m/s. The ship needs \(y\) seconds more to reach the coast from the current point . Then the value of \(x + y\) can be expressed as \(\frac{a\sqrt{3} +b}{c}\) where \(c\) is a prime number . Find the value of \(a+b+c\).

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