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.

Options

A. `10m//s`
B. `11m//s`
C. `12m//s`
D. `13m//s`

Answer

D

Explanation

Let us take `hati` along east `hatj` along north and `hatk` vertically down wards `vecv_(sb)=12 hatj+2 hak`
`vecv_(hs)=-4hati-5hatk,vecv_(hb)=vecv_(sb)+vecv_(hs)`
`|vecv_(hb)|=sqrt((4)^(2)+(12)^(2)+(-3)^(2))=13m//s`