Question

Two boats are heading away from shore. Boat 1 heads due north at a speed of 3.9 m/s relative to the shore. Relative to boat 1, boat 2 is moving 30° north of east at a speed of 1.8 m/s. A passenger on boat 2 walks due east across the deck at a speed of 1.2 m/s relative to boat 2. What is the speed of the passenger relative to the shore?

Answer 1

Answer;

The Passenger is moving  $60^\circ$  north of east with a speed of 5.53 m/s.

Explanation:

Let take east direction as positive x direction and north as positive y direction.

Let $v_1$be the velocity of the boat(1) with respect to shore and  $v_12$be the velocity of the boat(2) with respect to shore and $v_p$ bet the velocity of the person with respect to the shore

Now according to question we have

$\vec v_{21}=\vec v_2-\vec v_1\\\\1.8\cos30^\circ\vec i+1.8\sin30^\circ \vec j=\vec v_2-3.9\vec j\\\\v_2=1.8\cos30^\circ  \vec i+(1.8\sin30^\circ +3.9)\vec j\\v_2=1.55\vec i+4.8\vec j$

Now also we have,

$v_{p2}=\vec v_p-\vec v_2\\1.2\vec i=v_p-(1.55\vec i+4.8\vec j)\\\vec v_p=2.76\vec i+4.8\vec j$

Now the magnitude of velocity of person with respect to the shore is given by

$v_p=\sqrt{2.76^+4.8^2}\\v_p=5.53\ \rm m/s$

Hence the Passenger is moving  $60^\circ$  north of east with a speed of 5.53 m/s.

Answer 2

Answer:

The Passenger is moving 60^\circ60

∘

north of east with a speed of 5.53 m/s.