Question

Two ships leave a port from a point at the same time. One goes with a velocity of $3\, km / h$ along North-East making an angle of $45^{\circ}$ with East direction and the other travels with a velocity of $4 km / h$ along South-East making an angle of $15^{\circ}$ with East direction. Then, the distance between the ships at the end of two hours is

• A. $2 \sqrt{13}$
• B. $\sqrt{13}$
• C. $5$
• D. $10$

Answer 1

Answer: (A)

Distance travelled by ship $O A$ direction in $2\, h$ is $6\, km$ and $O B$ direction in $2\, h 138\, km$. $A B^{2}=O A^{2}+O B^{2}-20 A O B \cos \angle A O B$
$A B^{2}=(6)^{2}+(8)^{2}-2 \times 6 \times 8 \cos 60^{\circ}$
$A B^{2}=36+64-2 \times 6 \times 8 \times \frac{1}{2}$

$A B=\sqrt{100-48}=\sqrt{52}$
$A B=2 \sqrt{13}$