Question

Ship A is located 4.1 km north and 2.3 km east of ship B. Ship A has a velocity of 22 km/h toward the south and Ship B has a velocity of 40 km/h in a direction 38° north of east. What are the (a) x-component and (b) y-component of the velocity of A relative to B?

Answer 1

a) x component = -31.25 km/hr

b) y component = 46.64 km/hr

Step-by-step explanation:

Given data:

A position is 4km north and 2.5 km east to B

Ship A velocity = 22 km/hr

ship B velocity = 40 km/hr

A velocity wrt to velocity of B

`\vec{V_(AB)} =\vec{V_A} - \vec{V_B}`

`\vec{V_A} = 22 km/hr`

`\vec{V_B} = 40 cos38\hat{i} + 40sin 38 \hat{j}`

`= 31.52\hat{i} + 24.62 \hat{j}`

putting respective value to get velocity of A with respect to B

`\vec{V_(AB)} = -22 \hat {j} - (31.52\hat{i} + 24.62 \hat{j})`

`\vec{V_(AB)} = -31.52\hat{i} - 46.62\hat{j}`

a) x component = -31.25 km/hr

b) y component = 46.64 km/hr