Question

Ship A is located 4.2 km north and 2.7 km east of ship B. Ship A has a velocity of 22 km/h toward the south and ship B has a velocity of 39 km/h in a direction 36 ° north of east. What are the (a) x-component and (b) y-component of the velocity of A relative to B?

Answer 1

Answer:

(a) The x-component of velocity is 31.55 km/h

(b) The y-component of velocity is 44.92 km/hr

Solution:

As per the solution:

The relative position of ship A relative to ship B is 4.2 km north and 2.7 km east.

Velocity of ship A, $\vec{u_{A}}$ = 22 km/h towards South = $- 22\hat{j}$

Velocity of ship B, $\vec{u_{B}}$ = 39 km/h Towards North east at an angle of $36^{\circ}$ = $\vec{u_{B}} = 39sin36^{\circ} \hat{j}$

Now, the velocity of ship A relative to ship B:

$\vec{u_{AB}} = \vec{u_{A}} - \vec{u_{B}}$

$\vec{u_{A}} = - 22\hat{j}$

$\vec{u_{B}} = 39cos36^{\circ} \hat{i} - 39sin36^{\circ} \hat{j}$

Now,

$\vec{u_{AB}} = - 22\hat{j} +39cos36^{\circ} \hat{i} - 39sin36^{\circ} \hat{j}$

$\vec{u_{AB}} = 31.55\hat{i} - 44.92\hat{j}$