Ship A is located 4 km north and 3 km east of ship B. Ship A has a velocity of `20 kmh^-1` towards the south and ship B is moving at `40 kmh^-1` in a direction `37^@` north of east. X and Y-axes are along east and north directions, respectively

Options

A. Velocity of A relative to B is `(-32 hati-44hatj) km//h`
B. Position of A relative to B as a function of time is given by `r_(AB)= [(3 -32t) hati+(4 -44t) hatj] km`
C. Velocity of A relative to B is `(32 hati-44 hatj) km/h`
D. Position of A relative to B as a function of time is given by `(32t hati -44t hatj) km`

Answer

A, B

Explanation

`r_B=0` at `t=0`

`r_A=3 hati +4 hatj`
at `t=0`
`v_A=(-20 hatj)`
`v_B=(40 cos 37^@) hati+(40 sin 37^@) hatj`
`=(32 hati+24 hatj)`
`v_(AB)=(-32 hati-44 hatj) km//h`

At time `t=0, `
`r_(AB)=r_A-r_B=(3 hati+4 hatj)`
`:.` At time `t=t, `
`r_(AB)=(r_(AB)at t=0)+v_(AB)t`
`=(=3-32t) hati+(4-44t)hatj`