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

(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}`