Question

A ship is travelling due east at 30 km/hr and a boy runs across a deck in a south west direction at 10 km/hr. find the velocity of the boy relative to sea

Answer 1

Given info : A ship is travelling due east at 30 km/hr and a boy runs across a deck in a south west direction at 10 km/hr.

To find : The velocity of the boy relative to ship is..

solution : case 1 : ship is traveling due east at 30 km/hr

so, velocity of ship, $v_{ship}$ = 30 i

case 2 : boy runs across a deck in a South West direction at 10 m/s

∴ velocity of boy, $v_{boy}$ = 10(-cos45° i - sin45° j)

= -5√2i - 5√2 j

now, velocity of boy with respect to ship, $v_{boy,ship}$ = $v_{boy}$ - $v_{ship}$

= -5√2i - 5√2j - 30 i

= -(5√2 + 30)i - 5√2 j

magnitude of velocity of boy with respect to ship is √{(5√2 + 30)² + (5√2)²} = 37.7 km/hr.