A ship is travelling due east at a speed of `15 km//h.` Find the speed of a boat heading `30^@` east of north if it appears always due north from the ship.

Options

A. 30 km/h
B. `(15sqrt(3))/(2)km/h`
C. `10sqrt(3)km/h`
D. `20 km/h`

Answer

A

Explanation

where `v_(bg)` is the ship w.r.t. ground. Relative velocity of boat w.r.t. ship `upsilon_(bs)` is along north. `upsilon_(bs)` is resultant of `upsilon_(bg)` and `upsilon_(bg)` and `upsilon_(sg)` in opposite direction.

`upsilonb cos 30^(@)=upsilon_(bs)`
`upsilon sin 30^(@)=15 rArr upsilon 30 km//h`