A sailor in a boat, which is going due east with a speed of `8m//s` observes that a submarine is heading towards north at a speed of `12m//s` and sinking at a rate of `2 m//s`.The commander of submarine observes a helicopter ascending at a rate of `5 m//s` and heading towards west with `4 m//s`.Find the speed of the helicopter with respect to boat.

A sailor in a boat, which is going due east with a speed of `8m//s` ob

1.	A sailor in a boat, which is going due east with a speed of `8m//s` observes that a submarine is heading towards north at a speed of `12m//s` and sinking at a rate of `2 m//s`.The commander of submarine observes a helicopter ascending at a rate of `5 m//s` and heading towards west with `4 m//s`.Find the speed of the helicopter with respect to boat.
Answer» Taking east, north and vertically upward directions along `+x`, `+y` and `+z` axes respectively. For boat `vecV_(B)=8hati` Relative velocity of submarine w.r.t. boat `vecV_(S//B)=12hatj-2hatk` `:. vecV_(S)-vecV_(B)=12hatj-2hatk rArr vecV_(S)=8hati+12hatj-2hatk` Relative velocity of helicopter w.r.t. submarine `vecV_(H//S)=vecV_(H)-vecV_(S)` `5hatk-4hati=vecV_(H)-(8hati+12hatj-2hatk)` `vecV_(H)=+4hati+12hatj+3hatk` `\|vecV_(H)\|=sqrt(4^(2)+12^(2)+3^(2))=13m//s` `vecV_(H//B)=vecV_(H)-vecV_(B)=(4hati+12hatj+3hatk)-8hati= -4hati+12hatj+3hatk` `\|vecV_(H//B)\|=13m//s`

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