A ship sail with uniform velocity having components u and v eastward and northward respectively, relative to water. When the ship is at a distance d north from a submarine, a torpedo is fired from...

A ship sail with uniform velocity having components u and v eastward and northward respectively, relative to water. When the ship is at a distance d north from a submarine, a torpedo is fired from the submarine, with the intention of destroying the ship. Assuming that the torpedo moves uniformly with velocity w relative to water,

show that , if the torpedo strikes the ship, then w>u,

and find the time taken by the torpedo to move from the submarine to the ship.

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A ship sail with uniform velocity having components v and u eastward and northward respectively, relative to water. When the ship is at a distance d north from a submarine, a torpedo is fired from the submarine. The torpedo moves uniformly with velocity w relative to water in north word .

Let displacement component of the ship be x in north word direction.

Further let T be the time taken by ship to displaced from initial position to position whose north word component is x.

i.e

T= x/u   (i)

Torpedo has to cover distance (x+d) in north word. So Time taken by tarpedo to cover distance

`T_t` =`(x+d)/w`       (ii)

Tarpedo will hit ship if

`T_t<=T`

`(x+d)/w<=x/u`

`u(x+d)<=xw`

`=> ux<xw`

`u<w`

Also time can be calculated from either (i) or (ii).

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