Question

5. A ship is moving towards N-E with a velocity of
10 km/hr and to a passenger on board the wind
appears to blow from the north with a velocity of
10v2 km/hr. Actual velocity of the wind is
(1) 10 km/hr towards N-W
(2) 15 km/hr towards S-E
(3) 10 km/hr towards S-E
(4) 15 km/hr towards N-W​

Answer 1

answer : option (1) 10km/h towards N-W

explanation : ship is moving towards N-E with a velocity of 10km/hr.

so,velocity of ship, $v_s$ = 10(cos45° i + sin45 j)

= 5√2(i + j)

velocity of wind with respect to ship, $v_{ws}$ = -10√2 j

use application of relative velocity,

$v_{ws}=v_w-v_s$

or, -10√2 j =$v_w$ - 5√2(i + j)

or, -10√2i + 5√2(i + j) = $v_w$

or, -5√2 i + 5√2 j = $v_w$

or, $|v_w|$ = √{(-5√2)² + (5√2)²}

= √{50 + 50} = 10km/h

angle made by wind with x-axis , θ = tan-¹(5√2/-5√2) = 135° [ N-W ]

hence, actual velocity of wind is 10km/h towards N - W