Question

Ship $A$ is located $4km$ north and $3km$ east of ship $B$. Ship $A$ has a velocity of $20km{h}^{-1}$ towards the south and ship $B$ is moving $40km{h}^{-1}$ in a direction ${37}^{\circ }$ north of east. Take $x$ and $y$ axis along east and north direction respectively.

• A. Velocity of $A$ relation to $B$ is $-32\hat{i}-44\hat{j}$
• B. Position of $A$ relative to $B$ as a function of time is given by
  ${\overrightarrow{r}}_{AB}=(3-32t)\hat{i}+(4-44t)\hat{j}$
  where $t=0$ when the ships are in position described above.
• C. Velocity $B$ relative to $A$ is $-32\hat{i}-44\hat{j}$
• D. At some moment $A$ will be west of $B$

Answer 1

Answer: (A), (B)

The correct options are
A Velocity of $A$ relation to $B$ is $-32\hat{i}-44\hat{j}$
B Position of $A$ relative to $B$ as a function of time is given by

${\overrightarrow{r}}_{AB}=(3-32t)\hat{i}+(4-44t)\hat{j}$
where $t=0$ when the ships are in position described above.